The nature of those future security guarantees are another open question in the negotiations.
Efforts continue to assemble an international coalition prepared to offer ongoing military support to Kyiv in the event of a peace deal, though it is not yet clear what form that would take.
While the UK and France have proposed deploying international troops in Ukraine, several key defence players in Europe, including Germany and Italy, have expressed scepticism about that idea.
It is also not clear to what extent the US would be willing to underpin any future defence arrangements for Ukraine.
Following talks in London, Zelensky flew to Brussels to meet Nato chief Mark Rutte and EU chief Ursula von der Leyen, and will meet Prime Minister Georgia Meloni in Italy on Tuesday.
Moscow has also claimed talks with the White House have been constructive, despite little public indication it has moved on any of the goals set out by the Kremlin when it launched its full-scale invasion in February 2022.
On Sunday, Trump indicated that he viewed Zelensky as the main obstacle to securing a peace deal, something he has made a key foreign policy goal and which the president claimed he would be able to achieve rapidly during the 2024 presidential election campaign.
He told reporters that Russia was “fine” with the peace plan outlined to both sides by the US, but that he was a “little disappointed that Zelensky hasn’t read it”.
Almost simultaneously, Zelensky said he was waiting to briefed by his chief negotiator Rustem Umerov who had just taken part in three days of discussions with his US counterparts in Miami.
“Some issues can only be discussed in person,” said Zelensky.