Michael R. Bloomberg, New York City’s billionaire former mayor, spent $8 million as part of an unsuccessful effort to defeat Assemblyman Zohran Mamdani, a democratic socialist upstart, in June’s Democratic mayoral primary.

On Thursday, Mr. Bloomberg took a very different tack, meeting with Mr. Mamdani personally for the first time in what both sides described as a wide-ranging discussion about transportation issues, policing and how to staff City Hall.

“The conversation was definitely cordial and it was substantive actually,” said Howard Wolfson, a longtime political adviser to Mr. Bloomberg who joined the session with Mr. Mamdani, now the Democratic nominee and front-runner.

While Mr. Bloomberg’s aides were careful to stress that it was not an endorsement meeting, the get-together underscored the shifting terrain around Mr. Mamdani’s campaign for mayor as he maintains a double-digit polling lead and Election Day draws nearer.

Some Democrats who once viewed him warily are now taking a closer look, or searching for ways they could work with him. Mr. Mamdani, in turn, has shed some of his old leftist stances, even as he holds onto others.

Mr. Bloomberg’s views and actions are still carefully watched by the city’s business leaders, and many have been searching for a way to block Mr. Mamdani’s rise. Mr. Wolfson said that the men disagreed on several issues (he would not detail them), but had extensively discussed how best to hire good commissioners and deputy mayors.