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 criticized Hungary as the location of the prospective Trump-Putin talks, saying the country's Prime Minister Viktor Orban - perceived by Kyiv and many EU leaders as a Kremlin ally - could not make a positive contribution for Ukrainians.

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.

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.

However, 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 stated that Russia's position was unchanged without giving further details. Moscow has repeatedly demanded a complete withdrawal of Ukrainian troops from Ukraine's four regions in the southeast, which Kyiv and its allies argue amounts to a de facto capitulation.

According to Ukrainian political analyst Mykola Davyduik, the latest Trump-Zelensky meeting did not yield positive results for Ukraine, while Ivan Stupak, a former member of Ukraine's security and intelligence service, suggested the reports of acrimony were likely exaggerated.

As Trump continues his re-election campaign, his position on ending the war remains complex, urging Ukraine to stand firm while balancing diplomatic relations with Russia.