Emmanuel Macron has said a peace deal with Russia "must not mean a surrender of Ukraine" - as Donald Trump claimed Vladimir Putin's forces "want to end this war".
The US and French presidents met amid fragile relations between America and Europe and after Mr Trump launched a verbal attack on Ukrainian President Volodymyr Zelenskyy.
Meeting in the White House on the third anniversary of Russia's war in Ukraine, the French president said he and Mr Trump "made substantive steps forward during our discussions".
Mr Macron told reporters that Europe should do more to bolster defence in the continent.
However, he stressed Russia "is the aggressor" in the conflict and added: "President Putin violated the peace."
Peace must allow Kyiv 'sovereignty'
The French leader then said: "We want peace, he wants peace. We want peace swiftly, but we don't want an agreement that is weak."
"This peace must not mean a surrender of Ukraine or a ceasefire without guarantees," he added. "It must allow for Ukrainian sovereignty and allow Ukraine to negotiate with other stakeholders regarding the issues that affect it.
"It is also a country in which we need to shoulder our responsibilities so that we ensure security and stability for Ukraine and for the entire region.
"For Europeans, this is an existential issue."
Read more:
Trump and Macron's careful dance side-stepped divisions
'Get this war stopped'
At a news conference following the talks, Mr Macron said he "fully believes" there is a path forward in negotiations.
He also agreed "there is good reason for President Trump to re-engage with President Putin" - a week after the leaders had a 90-minute-long phone call.
Mr Trump added Russia would accept European troops in Ukraine as part of peacekeeping efforts, adding: "I specifically asked him (Putin) that question. He has no problem with it."
He told reporters: "When I got here, one of the first calls I made was to Putin and it was made with great respect. They want to end this war."
Mr Trump then explained he wants to "get this war stopped," whether that's through a ceasefire or a direct agreement - but when asked if Ukraine should give up territory as part of any deal, he said: "We'll see."
The news conference came as Mr Putin said he is ready to discuss Russia cutting its defence budget alongside the US, saying a mutual drop of 50% would be a "good idea".
The Russian president also touted a possible economic deal with the US, offering talks on a deal for its own rare earth metal supplies and for the sale of aluminium to American firms.
The US president is due to meet Sir Keir Starmer on Thursday, after the prime minister warned Mr Trump that a bad peace deal would be a "disaster for everyone".
Read more from Sky News:
Johnson criticises Trump's 'ghastly' Zelenskyy comments
US joins Russia to vote against UN resolution on Ukraine
Earlier on Monday, Mr Trump said he hoped Mr Zelenskyy would visit the US to sign a deal on Ukraine's rare earth minerals soon.
Just last week, in a bitter exchange of words, Mr Trump called Ukraine's leader a "dictator" and said he "better move fast or he is not going to have a country left" after Mr Zelenskyy had accused him of living in a Russian-made "disinformation space".
(c) Sky News 2025: Macron says Ukraine ceasefire 'must not mean surrender' - as Trump claims Russia wants 'to
Low-paid jobs at risk from Labour's tax increases on businesses
Sanctions against Russia have changed what Europe imports, but it's still worth billions to Putin
Care providers warn system is 'at breaking point'
Boris Johnson hits out at Donald Trump's 'ghastly' comments to Ukraine President Volodymyr Zelenskyy
Ex-Labour MP Mike Amesbury jailed for assault - but will still get £91,000 salary in prison
Pope Francis 'resumes some work' after 'slight improvement' in health, Vatican says
