When Mr. Bloomberg greeted his successor, he was flanked by his top lieutenants, who handed Mr. de Blasio an exhaustive guide to city agencies and the transition ahead.

Mr. de Blasio took a more low-key approach: None of his main advisers accompanied him to the session. By all accounts, the meeting was a cordial one — even though Mr. de Blasio wants to substantially alter Mr. Bloomberg’s approach to policing, education and economic development, and Mr. Bloomberg once referred to Mr. de Blasio’s policy ideas as “stupid.”

There were signs of détente. As he left City Hall, Mr. de Blasio embraced Howard Wolfson, Mr. Bloomberg’s chief political adviser, who attacked the de Blasio candidacy during the Democratic primary. (The two men had previously worked together on Hillary Rodham Clinton’s campaign for Senate in 2000.)

Mr. de Blasio called his meeting with Mr. Bloomberg “a very helpful conversation, very collegial.”

And Mr. Bloomberg, in an interview on CNN, said the two had agreed to meet periodically in the weeks before Mr. de Blasio took office on Jan. 1.

“I have a very big vested interest in making Bill de Blasio an even better mayor than I was,” Mr. Bloomberg said in the interview with the anchor Jake Tapper. “We’ve given them a lot to work with, as did our predecessors, but the bottom line is, I’m going to live in New York City, and I want Bill de Blasio’s administration to be successful.”

Still, Mr. Bloomberg offered a hint that his successor may find governing a metropolis to be slightly more complicated than the more abstract terrain of a political campaign.

“He’s got to make his own decisions,” Mr. Bloomberg said. “Some things will look easy, and then he gets into them, he’ll find them more difficult, and maybe he’ll change his mind.”