US President Donald Trump, who has promised to bring a quick end to the three-year-old war, has for weeks said he believes Russia's Vladimir Putin is committed to peace.
Sources have told Reuters the White House has grown wary of Putin's intentions in recent days, although Trump continues to signal publicly his belief that Putin wants to end the war.
"We will know soon enough, in a matter of weeks, not months, whether Russia is serious about peace or not. I hope they are," Rubio said at the end of a two-day NATO meeting.
"If this is dragging things out, President Trump's not going to fall into the trap of endless negotiations about negotiations," Rubio said.
"We're testing to see if the Russians are interested in peace. Their actions - not their words, their actions - will determine whether they're serious or not, and we intend to find that out sooner rather than later."
Russia rejected a US proposal in March for a full 30-day ceasefire after Ukraine said it would agree.
The warring sides then agreed to a limited pause in attacks on each other's energy infrastructure, which both accuse the other of violating.
The US says it is still in talks with both sides.
European countries want the US to demand Russia prove it is serious by signing up to a ceasefire, with some suggesting that an explicit deadline should be set.
Russia "owes an answer to the United States" which had "worked very hard to come up with a mediation effort and a ceasefire proposal," French Foreign Minister Jean-Noël Barrot said.
UK Foreign Minister David Lammy said Putin "continues to obfuscate, continues to drag his feet".
"He could accept a ceasefire now, he continues to bombard Ukraine, its civilian population, its energy supplies. We see you, Vladimir Putin, we know what you are doing," Lammy said.
German Foreign Minister Annalena Baerbock said Putin's talk of negotiations was "nothing but empty promises" and the Russian leader was "playing for time by raising ever new demands".
The foreign ministers of Canada and Estonia were among those calling for timelines for Russia to accept a ceasefire.
A senior State Department official said there was not necessarily a consensus on a timeline for increasing pressure on Russia but there was a recognition that "the sooner the better".
"There was consensus that Russia needs to do more, that Russia should agree to a ceasefire."
On the battlefront, a Russian missile attack killed at least 16 people, including six children, in a residential area of the Ukrainian city of Kryvyi Rih on Friday, local officials said, but Russia's Defence Ministry said it had targeted a military gathering in the city.
The strike in Zelenskiy's home town was one of Moscow's deadliest this year in the conflict, launched with the Kremlin's full-scale invasion of Ukraine in February 2022.
It occurred as Trump tries to end the war, damaged residential blocks and sparked fires, Serhiy Lysak, the regional governor, wrote on the Telegram messaging app.
The bodies of the dead and wounded could be seen lying on the pavement, one of them by a playground, in unverified videos circulating on Telegram, as grey smoke rose into the sky.
At least 50 people were wounded, the emergency services said, adding that the figure was growing. More than 30 people, including a three-month-old baby, were in hospital, Lysak said.
Russia's Defence Ministry, in a post on Telegram, said a "high-precision strike" had targeted "a meeting of unit commanders and Western instructors" in a city restaurant.
"As a result of the strike, enemy losses total up to 85 servicemen and officers of foreign countries, as well as up to 20 vehicles," the ministry said on Telegram.
