"We're not going to continue with this endeavour for weeks and months on end, so we need to determine very quickly now - and I'm talking about a matter of days - whether or not this is doable in the next few weeks," Rubio said in Paris after meeting European and Ukrainian leaders.
"If it is, we're in. If it's not, then we have other priorities to focus on as well."
Rubio said Trump was still interested in a deal but was willing to move on if there were no immediate signs of progress.
Trump promised during his election campaign to end the war within his first 24 hours in the White House.
He moderated that claim on taking office, suggesting a deal by April or May, as obstacles mounted.
Rubio's comments underline the mounting frustrations over a lack of progress in pushes to settle a growing list of geopolitical challenges.
They also follow Ukraine saying it has signed a memorandum with the US as an initial step towards clinching an agreement on developing mineral resources in Ukraine.
Although both had been poised in February to sign a deal for co-operation on natural resources, it was delayed after an Oval Office meeting between Trump and Ukrainian leader Volodymyr Zelenskiy turned into a shouting match.
"We are happy to announce the signing with our American partners," Yulia Svyrydenko, Ukraine's first deputy prime minister and economy minister, said on social media after the signing.
Thursday's memorandum of intent paves the way for an economic partnership deal and the setting-up of an investment fund for the reconstruction of Ukraine, she said.
The signing comes after officials in Kyiv worked to repair ties following the Oval Office episode, recognising that Ukraine needs US support in its war with Russia, which mounted a full-scale invasion of Ukraine in 2022.
The minerals deal is part of that effort, officials in Ukraine have said.
Trump said the accord itself could be signed next week, though the Ukrainian side gave no indication of when it expected to conclude the full deal.
An initial framework pact was agreed, but has never been signed.
"We have a minerals deal, which I guess is going to be signed on Thursday," Trump told reporters at the White House earlier.
He has pushed for a compact that gives the United States privileged access to Ukraine's natural resources and critical minerals in what he casts as repayment for military aid provided under former President Joe Biden.
"We're still working on the details," said Treasury Secretary Scott Bessent, seated beside Trump in the Oval Office, adding the signing could come by next Friday.
"It's substantially what we'd agreed on previously," he said.
The White House did not respond to a request for further details on the timing and contents of the agreement.
Zelenskiy had said both sides could sign the memorandum online.
"This is a memorandum of intent. And we have positive, constructive intentions," he told reporters in Kyiv, adding the US side had made the offer to sign the memorandum before the comprehensive deal, which would require ratification by Ukraine's parliament.
Earlier, Svyrydenko said the memorandum was the first stage to record the significant progress made by Kyiv and Washington in discussing the agreement.
