Moscow, Russia - The Kremlin on Monday said that Russian President Vladimir Putin still supported the idea of a truce in Ukraine, but many unanswered questions remained about how it would work.

US President Donald Trump has been pushing for a speedy ceasefire between Moscow and Kyiv since taking office, but his administration has failed to make a breakthrough despite talks with both sides.

"Putin does support the idea that a ceasefire is needed, but before that a whole range of questions have to be answered," Kremlin spokesman Dmitry Peskov told reporters on Monday.

"These questions are hanging in the air, so far no one has given an answer to them," he added, blaming the lack of progress on "the Kyiv regime's uncontrollability".

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Trump has meanwhile voiced frustration at the slow pace of talks, telling NBC news in March that he was "pissed off" with Putin.

On Sunday, he told reporters: "We're talking to Russia. We'd like them to stop. I don't like the bombing. The bombing goes on and on."

Putin rejected a joint US-Ukrainian proposal for an unconditional and full ceasefire in March, while the Kremlin has made a US-proposed truce in the Black Sea dependent on the West lifting certain sanctions.

US Secretary of State Marco Rubio on Friday said that Trump was not "going to fall into the trap of endless negotiations" with Russia over its three-year-long offensive.

"We will know soon enough, in a matter of weeks, not months, whether Russia is serious about peace or not," he said.