Volodymyr Zelenskyy has offered Donald Trump thousands of military drones in exchange for the Tomahawk missiles he has been seeking to step up Ukraine's defence against Russia.
The Ukrainian president travelled to Washington to seek more American weaponry, including the long-range missiles that could strike deep inside Russia, as his country continued to face relentless attacks on its energy network by the invading forces.
But the US president has indicated he is hesitant to provide the missiles, saying America may need to preserve its stocks.
"Hopefully we'll be able to get the war over with without thinking about Tomahawks," Mr Trump said.
The pair met a day after Mr Trump spoke to Russian President Vladimir Putin by phone, and later announced plans to meet him for talks in Budapest.
Russia initiated that phone call, according to the Kremlin. Mr Zelenskyy tweeted afterwards that Russia was "rushing to resume dialogue as soon as it hears about Tomahawks".
At the start of their meeting on Friday, local time, with media and cameras present, Mr Zelenskyy said he had a "proposition" for Mr Trump.
"Ukraine has thousands of our production drones, but we don't have Tomahawks," he said.
"And United States has Tomahawks and other missiles, very strong missiles. But they can have our thousands of drones. That's where we can work together."
Mr Trump said the men would discuss Ukraine's request but he "would much rather have them not need Tomahawks".
"I would much rather have the war be over, to be honest," Mr Trump said.
He also said he had "an obligation also to make sure that we're completely stocked up as a country because you never know what's going to happen in war and peace".
"That's the problem. We need Tomahawks and we need a lot of other things that we've been sending over the last four years to Ukraine."
Mr Trump made similar comments about the missiles after speaking to Mr Putin on Thursday. "We have a lot of them but we need them," he said.
Russia's full-scale invasion has been a catalyst for the rapid development of drone technology in Ukraine, and the US and Ukraine have been in talks about a drones "mega deal" for months.
US media reports have previously suggested both leaders were on board with the idea of Ukraine providing drones to the US in exchange for other weapons.
The Trump administration is meanwhile considering further economic penalties — including on purchasers of Russian energy — to increase pressure on Mr Putin.
A bill to authorise the president to impose sanctions is before the US Senate, though its details are still being worked out. About 85 of 100 senators have indicated they would support it if it went to a vote.
But Mr Trump has asked the leaders of the Republican-controlled Senate to hold off on progressing it for now.
"It may not be perfect timing," Mr Trump said after his call with Mr Putin. "It could happen in a week or two, but it's at my option, as you know."
The details of the summit in Budapest are still being arranged. No date has been set, but Mr Trump says it will likely take place "within two weeks or so".
Asked on Friday if he was concerned Mr Putin might simply be buying time, Mr Trump said: "Yeah I am, but, you know, I've been played all my life by the best of them and I came out really well."
Mr Zelenskyy spoke to reporters after the meeting, but said he and Mr Trump had agreed not to publicly discuss the missile request further. "We have to work on it more," he said.
Mr Trump left the White House without taking questions. He later wrote on social media that he had told both Mr Zelenskyy and Mr Putin "it is time to stop the killing, and make a DEAL".
"They should stop where they are. Let both claim Victory, let History decide!"
