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".

"We'll be involved in threes, but it may be separated," he said, adding the three leaders "have to get together".

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.

The US side was said to have echoed Russian talking points at the "volatile" meeting. It also reported that Trump tossed aside maps of the front line in Ukraine and insisted Zelensky surrender the entire eastern Donbas region to Putin.

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.

"Let both claim Victory, let History decide!" he said.

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.

Russia launched its full-scale invasion of Ukraine in February 2022. It currently controls about 20% of Ukrainian territory, including the southern Crimea peninsular Moscow annexed in 2014.

"We really didn't get what we wanted," Ukrainian political analyst Mykola Davyduik said of the latest Trump-Zelensky meeting.

"A few days after, we received some insights from the meeting and some threats and pressure that the Ukrainian side received there," he told the BBC.

But he added: "I don't think that Trump is fully and completely on Putin's side, and he is trying to play mediator... and that is his kind of style and how he behaves in such a situation."

Ivan Stupak, however, a former member of Ukraine's security and intelligence service (SBU), said reports of acrimony were likely exaggerated.

"I'm totally sure that this meeting was neutral, not negative, not a disaster," he told the BBC, adding that tempers sometimes flare, even between allies.

"It's not Disneyland, it's not a kindergarten. It's a meeting of two men and two leaders."

Just last month, Trump appeared to take a major shift in his position on ending the war by saying Kyiv could "win all of Ukraine back in its original form", referring to Ukraine's internationally recognised borders.

He said at the time that his position had changed "after getting to know and fully understand the Ukraine/Russia military and economic situation".

In a new twist on Monday, Trump said that Ukraine "could still win it", adding: "I don't think they will... Anything can happen... war is a very strange thing."

Trump had previously warned the process would likely involve Ukraine giving up some territory - an outcome Zelensky has consistently rejected.

The US president has been pressuring Nato nations, as well as China and India, to stop purchasing Russian oil in a bid to create further economic pressure on Moscow to end the conflict.

He also previously threatened Russia with tougher sanctions if Putin did not meet deadlines to make progress in ending the war, though he did not follow through with those threats.

Trump's public relations with Zelensky had also vastly improved in recent months, after an Oval Office meeting in February during which 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.