The United States of America v. Eric Adams was the first criminal indictment of a sitting mayor in the modern history of New York City. But the re-election of Donald J. Trump has invited questions about whether Mr. Adams might appeal to Mr. Trump for help in his federal corruption case — and whether Mr. Trump might entertain providing it.

In the weeks before the presidential election, Mr. Trump, a Republican and the first former president to be convicted of felonies, and Mr. Adams, the beleaguered Democratic mayor of the largest city in America, appeared to become unlikely bedfellows. Mr. Trump, who has publicly empathized with Mr. Adams, said that they were both the targets of politically motivated prosecutions.

Mr. Trump has been charged in four separate indictments and was convicted in Manhattan earlier this year of falsifying business records to cover up hush-money payments to a porn star. Mr. Trump has suggested without evidence that Mr. Adams is facing prosecution in his own criminal case, in which he is accused of conspiring with Turkish officials to receive illegal foreign campaign donations, because Mr. Adams had called out the Biden administration over the city’s migrant crisis.

At a charity event in Manhattan last month, Mr. Trump, standing at a lectern, turned to his right to address Mr. Adams: “We were persecuted, Eric. I was persecuted, and so are you, Eric.”

For his part, the mayor has been careful not to criticize Mr. Trump. In a move that seemed to break with others in the Democratic Party, Mr. Adams recently rejected the idea that Mr. Trump was a fascist, going so far as to defend him.

“I don’t think it’s fitting to anyone to state that the former president is equal to being Hitler,” said Mr. Adams, who was briefing reporters about security plans ahead of Mr. Trump’s rally at Madison Square Garden last month.