The Kremlin said it was awaiting details of a US-Ukrainian proposal agreed this week, and gave no indication of its readiness to stop fighting that has left tens of thousands dead in the past three years.
President Vladimir Putin visited Russian troops who have made gains against Ukrainian forces battling to keep Russian territory seized in an offensive last year.
Ukraine's President Volodymyr Zelensky said his country was ready to embrace a deal, and the United States had indicated it would issue a "strong" response if Putin refuses an accord.
"People are going to Russia right now as we speak. And hopefully we can get a ceasefire from Russia," Trump told reporters during an Oval Office meeting with Ireland's prime minister Micheal Martin.
The White House said that Trump's envoy Steve Witkoff, a mediator in the Gaza and Ukraine wars, would be in Moscow this week.
Trump on Wednesday did not mention whether he would speak with Putin, but added that there had been "positive messages" from Moscow, saying: "I hope he's going to have a ceasefire."
- 'Horrible bloodbath' -
Trump said that if the fighting could be halted, "I think that would be 80 percent of the way to getting this horrible bloodbath finished."
US Secretary of State Marco Rubio said Washington wanted Moscow's agreement with no strings attached. "That's what we want to know -- if they're prepared to do it unconditionally," Rubio said on a plane heading to a G7 meeting in Canada.
"If the response is, 'yes', then we know we've made real progress, and there's a real chance of peace. If their response is 'no', it would be highly unfortunate, and it'll make their intentions clear," he added.
Russian news agencies reported earlier that the heads of the CIA and Russia's SVR foreign intelligence agency had held their first phone call in several years.
Rubio was to give an update on the initiative at the G7 meeting in Charlevoix, Canada.
The defense ministers of France, Britain, Germany, Italy and Poland met in Paris to discuss how they could support Ukraine, and any ceasefire.
While the Kremlin made no immediate comment on the US-Ukraine proposal -- agreed at a meeting in Saudi Arabia on Tuesday -- the Russian foreign ministry said earlier this month that a temporary ceasefire would be unacceptable.
Trump said "devastating" sanctions were possible if Russia refused a deal but added: "I hope that's not going to be necessary."
- 'None of us trust the Russians' -
"I can do things financially that would be very bad for Russia. I don't want to do that because I want to get peace," Trump said.
The latest dramatic diplomatic swing came less than two weeks after Trump kicked Zelensky out of the White House complaining about the Ukrainian leader's attitude to US assistance.
Trump halted military aid and intelligence sharing with Kyiv, but that resumed after the truce proposal was agreed on Tuesday.
Trump had previously said he was ready to welcome Zelensky back to the White House and speculated he could speak with Putin this week.
In Kyiv, Zelensky said the United States would pile pressure on Moscow if it did not accept a ceasefire.
"I understand that we can count on strong steps. I don't know the details yet but we are talking about sanctions and strengthening Ukraine," Zelensky told reporters.
"Everything depends on whether Russia wants a ceasefire and silence, or it wants to continue killing people," the Ukrainian leader added.
He said Ukrainians had no confidence that fighting would stop. "I have emphasized this many times, none of us trust the Russians."
Ukraine is increasingly suffering on the battlefield, losing ground in the east and south of the country, where officials said eight people were killed on Wednesday.
Russia has also reclaimed territory in its western Kursk region, pushing back Ukrainian troops who staged a shock offensive last August.
Putin was shown on Russian television visiting troops in Kursk on Wednesday.
"I am counting on the fact that all the combat tasks facing our units will be fulfilled, and the territory of the Kursk region will soon be completely liberated from the enemy," Putin said.
Russian chief of staff General Valery Gerasimov said that 430 Ukrainian troops had been captured and Putin called them "terrorists."
Ukraine military commander-in-chief General Oleksandr Syrsky indicated that some forces in Kursk were pulling back to "more favorable positions."
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