UNITED NATIONS (Reuters) -The United States told the United Nations Security Council on Thursday that its proposal for a ceasefire in Ukraine was "Russia's best possible outcome" and President Vladimir Putin should take the deal.

The United States wants Russia to agree to a comprehensive 30-day land, air, sea and critical infrastructure ceasefire. A first round of direct talks between Russia and Ukraine on May 16 failed to reach an agreement on a ceasefire - which Moscow has said is impossible to achieve before certain conditions are met.

"We want to work with Russia, including on this peace initiative and an economic package. There is no military solution to this conflict," Acting Deputy U.S. Ambassador John Kelley told the Security Council. "The deal on offer now is Russia's best possible outcome. President Putin should take the deal."

U.S. President Donald Trump began his second term in January vowing to swiftly end Russia's three-year-old war in Ukraine. Kelley said the first U.S. step was to put forward a proposal for an immediate, unconditional and comprehensive ceasefire, which had been accepted by Ukraine, pending Russia's agreement.

"Since then, we have been urging Russia to accept a ceasefire," he said.

"If Russia makes the wrong decision to continue this catastrophic war, the United States will have to consider stepping back from our negotiation efforts to end this conflict," he warned, adding that Washington could also impose further sanctions on Russia.

Kelley said that after Trump and Putin spoke by phone last week, Russia was now expected to provide a term sheet broadly outlining its vision for a ceasefire in the conflict, which began when Moscow invaded its neighbor in February 2022.

"We will judge Russia's seriousness towards ending the war, not only by the contents of that term sheet, but more importantly, by Russia's actions," said Kelley, condemning Russia's recent attacks on Ukraine as not demonstrating "a desire for peace."

Russian Foreign Minister Sergei Lavrov said on Wednesday that Moscow had drafted a memorandum outlining a settlement position in the Ukraine war. But Ukraine said Moscow has not yet shared its proposal.

Russia's U.N. Ambassador Vassily Nebenzia said Moscow intended to continue serious, direct negotiations with Ukraine. Russia has suggested a second round of direct talks take place on Monday in Istanbul.

"The ball is in Ukraine's court: either talks, followed by peace, or the unavoidable defeat of Ukraine on the battlefield with different conditions for the conflict's end," Nebenzia told the Security Council.

Ukraine's Deputy U.N. Ambassador Khrystyna Hayovyshyn said Russia was "not signaling any genuine intention to stop its war" and urged countries to impose stronger sanctions on Moscow.

"Ukraine has consistently demonstrated commitment to diplomacy and remains open to any format that can yield tangible results," she said, but added that Kyiv would never recognize Russia's claim to any occupied Ukrainian territory.

"We will not tolerate interference in sovereign decisions, including our defense or alliances. There must be no appeasement of the aggressor. Such attempts only embolden future aggression," Hayovyshyn told the council.

(Reporting by Michelle Nichols; Editing by Caitlin Webber and Cynthia Osterman)