But in Ukraine, where officials are wary of offending President Trump, not so much. There, four meandering cases that involve Mr. Manafort, Mr. Trump’s former campaign chairman, have been effectively frozen by Ukraine’s chief prosecutor.

The cases are just too sensitive for a government deeply reliant on United States financial and military aid, and keenly aware of Mr. Trump’s distaste for the investigation by the special counsel, Robert S. Mueller III, into possible collusion between Russia and his campaign, some lawmakers say.

The decision to halt the investigations by an anticorruption prosecutor was handed down at a delicate moment for Ukraine, as the Trump administration was finalizing plans to sell the country sophisticated anti-tank missiles, called Javelins.