Ukrainian President Volodymyr Zelensky has said he would be ready to join Donald Trump and Vladimir Putin at a proposed summit in Hungary if he were invited.

The US and Russian presidents announced after their phone call on Thursday that they planned to hold talks on the war in Ukraine in Budapest, possibly in the coming weeks.

On Monday, Zelensky told reporters: If it is an invitation in a format where we meet as three or, as it's called, shuttle diplomacy... then in one format or another, we will agree.

Meanwhile, media reports suggest his White House meeting with Trump on Friday descended into a shouting match - with the US side urging Ukraine to accept Russia's terms to end the war.

Zelensky was guarded during his first press briefing since the talks, but still his comments made clear that there were large areas of disagreement between the two sides.

He described the meeting as frank, and said he had told Trump that his main aim was a just peace, not a quick peace.

He criticised Hungary as the location of the prospective Trump-Putin talks, saying the country's Prime Minister Viktor Orban - who is seen by Kyiv and many EU leaders as a Kremlin ally - could not do anything positive for Ukrainians or even provide a balanced contribution.

When asked by reporters on Friday if Zelensky would be involved in the meeting in Budapest, Trump said he wanted to make it comfortable for everybody.

Russian Foreign Minister Sergei Lavrov and US Secretary of State Marco Rubio held a constructive phone call on preparations for the Budapest summit, Moscow said on Monday.

Zelensky had hoped to secure US Tomahawk missiles to strike deep into Russia during his White House visit, but appeared to walk away empty-handed as Trump struck a non-committal tone on the matter.

Media reports suggested the atmosphere at the Trump-Zelensky meeting had been far more acrimonious than previously understood. The Financial Times reported that Trump had warned Zelensky that Putin would destroy Ukraine if he did not agree to its terms, citing sources familiar with the conversation.

Trump wrote on social media shortly after the meeting that Russia and Ukraine should stop where they are - referring to the current, vast front line. Zelensky reacted by saying that he was ready for an immediate ceasefire - but insisted that Ukraine will not gift anything to the aggressor.

Commenting on the proposed freezing of the front line, Putin's spokesman Dmitry Peskov said on Monday that Russia's position was unchanged - without giving any further details.

Moscow has repeatedly demanded a complete withdrawal of Ukrainian troops from Ukraine's four regions in the south-east - Donetsk, Luhansk (collectively known as Donbas), Zaporizhzhia and Kherson - as well as several other tough conditions. Kyiv and its allies say the demands are tantamount to a de facto capitulation.

Trump's public relations with Zelensky had also vastly improved in recent months, after an Oval Office meeting in February where he and Vice-President JD Vance berated the Ukrainian president on live television. During his re-election campaign, Trump claimed he would be able to end the war in Ukraine within days but has since admitted resolving the conflict has been more challenging than any he has been involved in since returning to office.