Zelensky suggests Ukraine could provide drones to the US in exchange for long-range Tomahawk missiles, during talks with Trump at the White House
The Ukrainian president congratulates Trump on the Gaza ceasefire deal, and tells him: "I think we can end this war with your help"
Trump warns that giving Ukraine Tomahawk missiles "could mean bigger escalation" and that "a lot of bad things can happen"
The US president earlier signalled he might be willing to give Tomahawks to Ukraine, but after speaking to Vladimir Putin yesterday said: "We need them too… so I don't know what we can do about that"
Trump and Putin agreed to meet in Hungary during their phone call, with fresh talks between the leaders' advisers planned for as early as next week
Edited by Caitlin Wilson, with Bernd Debusmann Jr reporting from the White House
John Sudworth
North America Correspondent, reporting from Kyiv
Oleksandr, or Alex, gestures at his destroyed car
Alex is another resident of the neighbourhood I visited in Kyiv.
He was at home at the time of the missile attack and tells me that, he’d got so used to the sound of bombardment that he almost didn’t bother to look outside.
When he did, he found his car, parked just across the street from the point of impact, bent and broken by the blast wave.
"I think they just hate us as a nation because we do not obey them," he tells me.
There is no meaningful military justification for striking residential communities like this one, he points out.
The intention, he says, is to spread such fear that the Ukrainians can be forced to concede before going on to insist that that will never happen.
As for the summit, he is also convinced that President Trump is being played by Russia.
"Do you think he’ll be disappointed by Vladimir Putin once again?" I ask.
"For sure," he replies. "100% sure."John Sudworth
Reporting from Kyiv
Volodymyr has been repairing the store he owns after it was destroyed in a Russian missile strike
The two presidents' meeting in Washington is a long way from the suburbs of Kyiv, where I meet Anna and Volodymyr still busy repairing the small store they own after it was obliterated last month.
Two Russian missiles struck this neighbourhood, destroying homes and businesses and leaving a number of people injured although remarkably – given the scale of the destruction – no loss of life.
Here, even a simple question about the Russian leader behind the onslaught they experienced that September night elicits a strong reaction.
"We appreciate all support," Volodymyr begins to tell me, when I ask him about President Trump’s announcement that he is going to hold another summit meeting with President Putin.
But then he has to step away as the tears well up. After a long pause he composes himself and begins again.
"Truth and democracy will win, and all the terrorism and evil will disappear," he says, still struggling with the emotion.
"We just want to live, we don't want to give up, we just want them to leave us alone."
There is no point negotiating with Putin, he insists.
"We don’t trust Putin anymore," Anna agrees. "We don’t trust him at all."
Like everyone in Ukraine, they're tired of this war. They desperately want to believe that peace is possible.
But they think the US president is, once again, being taken for a ride.
Tom Bateman
US State Department correspondent
I just asked Zelensky whether Trump gave him any further assurances over a US security guarantee for Ukraine.
He reiterated his position that such a guarantee was crucial for Ukraine, but declined to say whether he got any new details from Trump.
"We need strong security guarantees," Zelensky told me. "Our nation is afraid that if we will have [cease]fire, we need security guarantees from the US [so] Putin will not come again with aggression."
Some European countries have already offered forces for Ukraine to help shore up any Trump-brokered truce. But Kyiv fears without American backing these would not be enough to deter Russia from any future re-invasion of Ukraine.
This issue of US guarantees was a focal point of talks when European leaders came here to the White House in August after the Alaska summit, but the extent of any assurances from the Trump administration remained unclear.
Zelensky is asked what he thinks Putin wants to get out of his meeting with Trump in Budapest. Does he want a deal or is he just buying time, a reporter asks.
"I don't know," Zelensky says. But he adds that the prospect of Ukraine having Tomahawks has caused Russia to be "afraid because it is a strong weapon."
"They know what kind of weapons we have and they understand that combination with Tomahawks… they understand what we can do," he says.
Zelensky is asked if he is leaving Washington today more optimistic that Ukraine will get the Tomahawks.
"I am realistic," he says.
Zelensky says for the sake of each nation, he agrees with Trump that he and Putin must stop fighting and start talking about a just and lasting peace.
He says he's open to bilateral or trilateral meetings, or any formats that can "bring us closer to peace".
Speaking in Ukrainian, President Zelensky tells reporters that Ukraine is unable to fight using its current air defence systems against Russian ballistic missiles.
"It is very difficult," he says.
Zelensky adds that Ukraine needs to put pressure on Russia in the form of a weapons package to achieve its objectives.
The Ukrainian president later adds in English that he hopes the US can take Ukrainian drones. It comes after he suggested Ukraine could offer its drones in exchange for Tomahawk missiles.
Zelensky appears to suggest there was no progress in his appeal to the US for Tomahawk long-range missiles.
"This is the position of the Americans for today but nobody cancelled this topic," he says. "We have to work on it more."
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'Putin hates me,' says Zelensky
Zelensky is asked why he thinks Putin is avoiding him.
"It's not a secret," Zelensky answers. As Trump said, Putin "hates me".
When asked if he hates Putin back, Zelensky responds that Putin wants to kill all of his people, so it's understandable that he would have a similar feeling towards Putin.
"It's not about feelings… they [Russians] attacked us – and it's the enemy…. certainly, we hate the enemy", Zelensky adds in Ukrainian.
President Zelensky is asked about his thoughts on whether Ukraine can take back the territory it lost from Russia.
He answers that it is a very difficult and sensitive topic.
Russia wants to occupy the whole of Ukraine, he says. In the event of a ceasefire, he says that Russia wants a deal signed that sees it keep territory it has gained. This, he says, is opposite to his position on the matter.
"First, we need a ceasefire," he adds. "So we need to sit and speak and understand where we are. That is the most important step."
Zelensky adds that Trump understands the importance of territory in any ceasefire conversation.
Zelensky apologises for being late to the news conference and says he was speaking on the phone with several allies after his meeting with Trump.
He spoke with the leaders of the EU, Italy, the UK and Nato among others. He says he told them about how the two sides discussed security guarantees.
"We trust President Trump that he wants to finish this war, and it's difficult," Zelensky says.
"It's a very tough solution."
But, he adds, he also knows that brokering a ceasefire in the Middle East was a difficult situation and Trump managed that.
He says he hopes Trump will be able to help end the war in Ukraine as well.
Zelensky says he and Trump talked about long-range weapons, but both decided not to make any public statements about that conversation.
He says this is "because the United States does not want an escalation".
It is unclear if the Ukrainian president means that the weapons are off the table, or if information about the use of missiles will not be discussed publicly.
Zelensky starts speaking Ukrainian at the podium, then says "Oops, sorry, I forgot I'm in the United States" and switches to English.
He tells reporters it was a long and productive meeting with Trump, with lots to discuss.
He thanks Trump and his team for the conversation.
Zelensky has arrived to a podium set up outside the White House to answer questions after his meeting with Trump. You can follow along by clicking watch live at the top of this page.
Trump has left the White House now, heading for his private Mar-a-Lago home in Florida for the weekend.
He did not speak to the assembled press eager to ask questions about his meeting with Zelensky.
It's a beautiful autumn late afternoon here in Washington and we are waiting for Zelensky to speak at a park outside the White House.
News cameras and microphones are being step up now for his first public comments since closed-door discussions with Trump.
You can see his comments by clicking watch live at the top of this page.
Myroslava Petsa
BBC News Ukrainian, reporting from the White House
At this White House meeting, the Ukrainian delegation were treated to a formal lunch of roast chicken and apple and caramel cake with clementine ice cream for dessert – a far cry from the screaming match the world witnessed back in February.
And while toasting and tasting, the American and Ukrainian teams discussed the hit points that Ukraine would like to strike, if the US provides Kyiv with long-range missiles.
Before lunch, the press were able to ask President Trump all sorts of questions. And the main topic of conversation was the Tomahawks – whether or not America was willing to provide them and put more pressure on Putin to engage in real peace negotiations.
We've just seen Zelensky head out the door of the White House to his vehicle, which was waiting just outside.
That marks the end of his closed-door working lunch with Trump, following 40 minutes of questions from the press a little earlier.
As Zelensky prepares to depart Washington DC after meeting with Trump, he will head back to a country torn apart by constant bombardment.
The pictures below show the devastation that Russian strikes left in the Ukrainian regions of Kherson and Druzhkivka last night.
While we wait to hear more from the leaders after their lunch meeting, let's take a look back at what we know about the Russia-Ukraine war.
Fighting has raged in Ukraine since Russia launched a full-scale invasion in February 2022.
Over the past year, Russian forces have slowly expanded the amount of territory they control, mostly in the east of Ukraine, and have continued their recent barrage of air strikes on Kyiv and other key Ukrainian cities.
In eastern Ukraine, Russia's war machine has been churning mile by mile through the wide open fields of the Luhansk and Donetsk regions – also known as the Donbas – surrounding and overwhelming villages and towns.
It has been trying to gain full control of the area along with two more regions to the west – Zaporizhzhia and Kherson.
Further north, Russia has been pushing towards Kupyansk in the east of the Kharkiv region, as part of its efforts to capture the whole of Luhansk and encircle northern Donetsk.
Meanwhile, Russia has continued to bomb Ukrainian cities, launching 574 drones and 40 missiles on the night of 20 August, external – which the Institute for the Study of War described as the third-largest strike of the war so far.
It has also targeted Ukraine's rail infrastructure – a central pillar of Ukraine's war effort and a powerful national symbol of resilience – with multiple attacks in recent months.
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