Not that long ago, an 11th-hour revelation that the Justice Department was criminally investigating a candidate like Andrew M. Cuomo would have been enough to kill or at least seriously maim a mayoral campaign.

So it was something of a mile-marker in Democrats’ growing distrust of the Trump administration that when news of the inquiry into the New York City front-runner broke late Tuesday, not even Mr. Cuomo’s rivals could quite be sure who would benefit politically.

On one hand, the inquiry appeared to echo his rivals’ criticisms of Mr. Cuomo as dishonest and corrupt. It centers on whether Mr. Cuomo lied to Congress about decisions he made as governor during the coronavirus pandemic.

Several candidates seized on the Justice Department’s action to argue that New Yorkers should not replace Mayor Eric Adams, whose administration was upended by a federal inquiry, with a second politician who might have reasons to curry favor with Mr. Trump.

“We cannot trade one compromised mayor for another,” said Zellnor Myrie, a state senator from Brooklyn.

But Democrats’ conviction that President Trump is abusing the Justice Department is now so deep that party leaders and even some of Mr. Cuomo’s critics said that being a target could help him in the June 24 mayoral primary in the nation’s largest Democratic city.