Kremlin spokesperson Dmitry Peskov said it was important not to "get ahead" of the question of responding to the ceasefire proposal.
He told reporters on Wednesday that Moscow was awaiting "detailed information" about it from the US and suggested that Russia must get that first before it can take a position.
Arms deliveries to Ukraine have already resumed through a Polish logistics centre, the foreign ministers of Ukraine and Poland announced Wednesday.
The deliveries go through a NATO and US hub in the eastern Polish city of Rzeszow that has been used to ferry Western weapons into neighbouring Ukraine about 70km away.
The American military help is vital for Ukraine's shorthanded and weary army, which is having a tough time keeping Russia's bigger military force at bay.
But for Moscow, more American aid spells potentially more difficulty in achieving its war aims and likely will be a tough sell in Moscow for Washington's peace efforts.
Meanwhile, an intensifying Russian effort to push Ukrainian forces out of its Kursk region has yielded breakthroughs in recent days, Ukrainian soldiers told The Associated Press.
The fighting has escalated as ceasefire talks come to a head, with Moscow intent on taking back its territory and Kyiv determined to hold onto it as a bargaining chip in any negotiations.
Ukrainian forces made a daring raid into the Russian region last August in the first foreign occupation of Russian territory since World War II.
They have held on despite intense pressure from tens of thousands of Russian and North Korean troops.
Recent fighting reportedly has focused on the Kursk town of Sudzha, which is a key Ukrainian supply hub and operational base.
Ukrainian soldiers said that the situation is dynamic and fighting continues in and around the town, but three of them conceded Russian forces were making headway.
Russian state news agencies RIA Novosti and Tass reported Wednesday that the Russian military have entered Sudzha.
It was not possible to independently verify either side's claims.
Inside Ukraine, Russian ballistic missiles killed at least five civilians, officials said on Wednesday.
US President Donald Trump wants to end the three-year war and pressured Zelenskiy to enter talks.
The suspension of US assistance came days after Zelenskiy and Trump argued about the conflict in a tense White House meeting.
US Secretary of State Marco Rubio, who led the American delegation to Tuesday's talks in Saudi Arabia, said that Washington would present the ceasefire offer to the Kremlin, which has opposed anything short of a permanent end to the conflict and has not accepted any concessions.
"We're going to tell (the Russians) this is what's on the table. Ukraine is ready to stop shooting and start talking. And now it'll be up to them to say yes or no," Rubio told reporters after the talks.
"If they say no, then we'll unfortunately know what the impediment is to peace here."
Trump's special envoy, Steve Witkoff, is expected to travel this week to Moscow, where he could meet Russian President Vladimir Putin, according to a person familiar with the matter but not authorised to comment publicly.
The person cautioned that scheduling could change.
French President Emmanuel Macron welcome the US-Ukraine agreement and said on X that "the ball is now clearly in Russia's court".
The outcome of the Saudi Arabia talks "puts the ball back in Russia's court and places the onus on Washington to persuade Moscow to accept and implement the ceasefire," John Hardie, a defence analyst and deputy director of the Russia Program at the Foundation for Defense of Democracies, a Washington-based research institute.
"Moscow will present itself as co-operative, but may push for agreement on basic principles for a final peace deal before agreeing to a ceasefire," he said.
"Russia may also insist on barring Western military aid to Ukraine during the ceasefire and on Ukraine holding elections ahead of a long-term peace agreement."
with AP
