The two others involved in the effort have somewhat questionable pasts: Mr. Sater, 50, a Russian-American, pleaded guilty to a role in a stock manipulation scheme decades ago that involved the Mafia. Mr. Artemenko spent two and a half years in jail in Kiev in the early 2000s on embezzlement charges, later dropped, which he said had been politically motivated.

While it is unclear if the White House will take the proposal seriously, the diplomatic freelancing has infuriated Ukrainian officials. Ukraine’s ambassador to the United States, Valeriy Chaly, said Mr. Artemenko “is not entitled to present any alternative peace plans on behalf of Ukraine to any foreign government, including the U.S. administration.”

At a security conference in Munich on Friday, Mr. Poroshenko warned the West against “appeasement” of Russia, and some American experts say offering Russia any alternative to a two-year-old international agreement on Ukraine would be a mistake. The Trump administration has sent mixed signals about the conflict in Ukraine.

But given Mr. Trump’s praise for Mr. Putin, John Herbst, a former American ambassador to Ukraine, said he feared the new president might be too eager to mend relations with Russia at Ukraine’s expense — potentially with a plan like Mr. Artemenko’s.

It was late January when the three men associated with the proposed plan converged on the Loews Regency, a luxury hotel on Park Avenue in Manhattan where business deals are made in a lobby furnished with leather couches, over martinis at the restaurant bar and in private conference rooms on upper floors.

Mr. Cohen, 50, lives two blocks up the street, in Trump Park Avenue. A lawyer who joined the Trump Organization in 2007 as special counsel, he has worked on many deals, including a Trump-branded tower in the republic of Georgia and a short-lived mixed martial arts venture starring a Russian fighter. He is considered a loyal lieutenant whom Mr. Trump trusts to fix difficult problems.