Both Ukraine and Russia accused each other of thousands of strikes and violating the Kremlin's unilateral ceasefire during the Easter celebrations.
"We always have a positive attitude towards a truce, which is why we came up with such an initiative, especially since we are talking about the bright Easter days," Putin told a state TV reporter on Monday.
"We have always talked about this, that we have a positive attitude towards any peace initiatives. We hope that representatives of the Kyiv regime will feel the same way."
Washington had said it would welcome an extension of the truce, and Ukrainian President Volodymyr Zelenskiy reiterated several times Ukraine's willingness to agree a pause strikes on civilian infrastructure for 30 days in the war.
Putin said Russia has to carefully study this and other proposals.
The Kremlin also said on Monday that it was satisfied with US President Donald Trump's administration ruling out NATO membership for Ukraine, but declined to comment on his hopes for a peace deal.
Trump, seeking to be remembered as a peacemaker, has repeatedly said he wants to end the "bloodbath" of the three-year conflict in Ukraine - which his administration casts as a proxy war between the United States and Russia.
US envoy General Keith Kellogg said on Sunday that NATO alliance membership was "off the table" for Ukraine. Trump has said past US support for that was a cause of the war.
"We have heard from Washington at various levels that Ukraine's membership in NATO is excluded," Kremlin spokesman Dmitry Peskov told reporters.
"Of course, this is something that causes us satisfaction and coincides with our position."
Ukrainian membership of the US-led alliance would threaten Russian interests, Peskov added. "And, in fact, this is one of the root causes of this conflict."
