The prospect of a trilateral meeting mediated by the US came after US President Donald Trump met Putin in Alaska, before hosting Zelensky and other European leaders at the White House.
Zelensky has stated his willingness to meet Putin in “any format”.
Hungarian Foreign Minister Peter Szijjarto offered Budapest as a possible venue for such a summit on Thursday.
Hungary’s Prime Minister Viktor Orban has maintained close ties with Moscow and has frustrated EU efforts to support Ukraine in the war with Russia in the past – so may not be viewed by all as a neutral host.
Speaking to reporters on Thursday morning, Zelensky did not discuss Hungary’s offer – but said he had asked Trump to pressure Hungary into unblocking negotiations for Ukraine to join the EU.
“Trump promised that his team would work on this,” he said.
The Ukrainian leader also said that Russian forces were massing on the southern front line in the Zaporizhzhia region – one of four regions of Ukraine that Russia now claims as its own.
“We can see that they continue transferring part of their troops from the Kursk direction to Zaporizhzhia.”
Ukraine’s air force counted 614 aerial vehicles among Russia’s overnight attacks, 577 of which it said it had stopped.
Foreign Minister Sybiha said this included a mix of drones, hypersonic, ballistic, and cruise missiles.
“One of the missiles struck a major American electronics manufacturer in our westernmost region, leading to serious damage and casualties,” he wrote on social media on Thursday.