Ukrainian President Volodymyr Zelenskiy hailed Monday's extraordinary summit at the White House with Trump as a "major step forward" towards ending Europe's deadliest conflict in 80 years and towards setting up a trilateral meeting with Russia's Vladimir Putin and the US president in the coming weeks.
Flanked by the leaders of allies including Germany, France and Britain at the summit, Zelenskiy's warm rapport with Trump contrasted sharply with their disastrous meeting at the Oval Office in February.
But beyond the optics, the path to a lasting peace remains deeply uncertain and Zelenskiy may be forced to make painful compromises to end a war that analysts say has killed or wounded more than 1 million people.
And despite the temporary sense of relief in Kyiv, there was no let-up in the fighting.
Russia launched 270 drones and 10 missiles in an overnight attack on Ukraine, the Ukrainian air force said, the largest in August.
The energy ministry said Russia had targeted energy facilities in the central Poltava region, home to Ukraine's only oil refinery, causing big fires.
Zelenskiy said on Tuesday his officials were working on the content of the security guarantees.
Russia has made no explicit commitment to a meeting between Putin and Zelenskiy.
Foreign Minister Sergei Lavrov said on Tuesday Moscow did not reject any formats for discussing the peace process in Ukraine but that any meeting of national leaders "must be prepared with utmost thoroughness".
Putin has warned that Russia will not tolerate troops from the NATO alliance on Ukrainian soil.
He has also shown no sign of backing down from demands for territory, including land not under Russia's military control, following his own summit talks with Trump last Friday in Alaska.
Trump has not specified what form US security guarantees could take, and backed away from insisting that Russia agree to a ceasefire before any peace negotiations kick off in earnest.
The US president has also told Ukraine to forget about regaining control of Crimea, which was annexed by Russia in 2014, or joining NATO.
Former Russian President Dmitry Medvedev said Zelenskiy and his allies had "failed to outplay" Trump, posting on X that "Europe thanked & sucked up to him".
The last direct talks between Russia and Ukraine took place in Turkey in July while Putin also declined Zelenskiy's public invitation to meet him face-to-face in May.
"President Trump has now opened the door to the negotiating room for him, and Putin must now enter it," German Foreign Minister Johann Wadephul told the Deutschlandfunk radio broadcaster, and if not, sanctions must be intensified.
On what security guarantees could be offered to Ukraine: "We are working flat out to specify this."
Ukraine's allies will hold talks in the so-called "Coalition of the Willing" format on Tuesday to discuss the way forward.
NATO Secretary-General Mark Rutte, who also attended Monday's talks, said NATO membership for Ukraine was not under discussion but that there was a discussion on "Article 5"-type security guarantees for the country.
Article 5 of NATO's founding treaty enshrines the principle of collective defence, in which an attack on any of its 32 members is considered an attack on all.
