But Mr. Yatsenyuk, who stepped down as prime minister last year in a domestic political dispute with President Petro O. Poroshenko, nonetheless sees some hope. He takes solace in Mr. Trump’s decision not to ease sanctions and said his meetings with administration officials this week were encouraging. “We are on the agenda,” he said.

While Ukraine’s Washington lobbyists have tried and so far failed to secure a meeting between Mr. Poroshenko and Mr. Trump, the president did call the Ukrainian leader in February. More significantly, Mr. Trump hosted Ukraine’s foreign minister, Pavlo Klimkin, at the White House last week on the same day the president met with Sergey V. Lavrov, the Russian foreign minister.

Still, the way the White House handled the meeting with Mr. Klimkin was striking. While Mr. Lavrov’s visit was listed on the public schedule, the White House made no mention of Mr. Klimkin’s. It did not become public until a day later when Mr. Trump mentioned it on Twitter: “Yesterday, on the same day- I had meetings with Russian Foreign Minister Sergei Lavrov and the FM of Ukraine, Pavlo Klimkin. #LetsMakePeace!”

As a former prime minister, Mr. Yatsenyuk was not able to secure a meeting with the president or secretary of state, but he met this week with Fiona Hill, the top White House adviser on Russia, and Andrea Thompson, the national security adviser to Vice President Mike Pence. On Capitol Hill, he met with sympathetic lawmakers like Senator Ted Cruz, Republican of Texas. He also met with Mr. Obama while in town.

Mr. Yatsenyuk wants Mr. Trump to see Mr. Putin as he does. “I don’t believe the U.S. and Russia could get along,” he said. “You are not just on different sides of the aisle, you guys are in different universes. You were, you are and you will be adversaries. You stick to the values of the free world. He sticks to the values of dictatorship and autocracy.”

For the president, Russia has become a domestic political millstone because of Moscow’s meddling in last year’s election and multiple investigations into whether Mr. Trump’s campaign associates had anything to do with that. Mr. Trump has adamantly denied any collusion and no concrete evidence has emerged publicly, but a new special counsel was appointed this week.

Mr. Yatsenyuk said Russian interference in elections in the United States as well as those in France, the Netherlands and other European countries should make clear what Mr. Putin’s real aim is. “He wants to set a fire to the whole house of the free world, to distract everyone,” he said.

Where Mr. Yatsenyuk holds out hope is that Mr. Trump will eventually view Mr. Putin as a challenge to his manhood. “The only language that President Putin understands is the language of strength,” he said. “The good news is that President Trump wants to be a very strong, masculine leader. And you can’t have two masculine folks on one block.”