US President Donald Trump has spoken of his optimism for a Ukraine ceasefire - saying he thinks "it's going to end" - after his Budapest meeting with Russian President Vladimir Putin fell through.
The planned summit between President Trump and Putin was put on hold on Tuesday after Moscow's rejection of an immediate ceasefire in Ukraine cast a cloud over attempts at negotiations.
Trump announced last week he and Putin would meet soon in Budapest, Hungary, to try to bring an end to the war in Ukraine.
But Putin has been unwilling to consider concessions.
Moscow has long demanded that Ukraine agree to cede more territory before any ceasefire.
Speaking from the Oval Office on Tuesday, President Trump reiterated previous remarks that he wanted Russian and Ukrainian soldiers to "go home" and "pull back" to the battle lines.
Russia controls all of the province of Luhansk and about 75 per cent of neighbouring Donetsk, which together make up the Donbas region.
President Trump said both countries were losing up to 7,000 soldiers a week, but remained optimistic that peace would eventuate.
"I'll see what happens. But we did all of these great deals, great peace deals," he said.
Asked if he still saw a chance of a ceasefire, Trump said "I do" and "I think it's going to end".
"It's a vicious war. It doesn't really affect us," Trump said.
"The war would have never happened if I were president. Would have never, not even a million years, and Putin knows that would have never happened. But it did happen."
Russia reiterated its long-standing terms for a peace deal in a private communique known as a "non-paper" that it sent to the US last weekend, according to two US officials and two people familiar with the situation.
The communique reaffirmed Russia's demand for full control of the long-contested eastern Donbas region, according to one official, effectively rejecting Trump's call for a ceasefire to commence with a freeze of the frontlines at their prevailing locations.
A senior White House official told Reuters "there are no plans for President Trump to meet with President Putin in the immediate future" after Secretary of State Marco Rubio and Russian Foreign Minister Sergei Lavrov had a "productive call" but opted against an in-person meeting.
European leaders called on Washington on Tuesday to hold firm in demanding an immediate ceasefire in Ukraine, with present battle lines to serve as the basis for any future talks.
NATO said Secretary General Mark Rutte travelled to Washington on Tuesday for talks with Trump that two sources familiar with the matter said would take place on Wednesday.
A Western official, speaking on condition of anonymity, said Rutte planned to present to Trump the European views on a ceasefire and any subsequent peace negotiations.
Trump, who last week spoke by phone to Putin and met Ukrainian President Volodymyr Zelensky, had hoped for another high-profile session with the Russian leader after their August summit in Alaska failed to advance negotiations.
But the two sides postponed a preparatory meeting between Rubio and Lavrov that had been expected to take place in Budapest on Thursday.
Lavrov and Rubio spoke by phone on Monday. Lavrov said the place and the timing of the next Trump-Putin summit was less important than the substance of implementing the understandings reached in Alaska.
The Kremlin said there was no clear date and that "serious preparation" for a summit was needed, which may take time.
"Listen, we have an understanding of the presidents, but we cannot postpone what has not been finalised," Kremlin spokesman Dmitry Peskov said. "Neither President Trump nor President Putin gave exact dates."