Lobbyists, those with business before the city and others who regularly engage with both sides of city government, have taken notice of the rapid change in the relationship from the relatively placid days under Mr. Johnson’s predecessor, Melissa Mark-Viverito, an early supporter of Mr. de Blasio’s who gained her position in part because of a push from the newly elected mayor.

Mr. Johnson, by contrast, rose to the position of speaker with the support of county Democratic leaders, and he rode a wave of simmering resentment among Council members at their treatment by the de Blasio administration. Those sentiments boiled over after comments by Deputy Mayor Alicia Glen, during a deposition in a lawsuit over housing segregation, in which she referred to Council members as “not that smart.” Council members were not amused.

Several lobbyists and political observers note the benefits of greater Council independence: another set of ears to listen to concerns; a new way to exert pressure on City Hall.

“The Council is supposed to be a counterbalance to the mayor, and we haven’t had that in a long time,” said Suri Kasirer, a city lobbyist. “I think it’s good government.”

Eric F. Phillips, a spokesman for the mayor, pointed to areas of agreement with Mr. Johnson, including a decision to site a jail in the Bronx, part of the plan to close Rikers Island. “Their partnership on a frequently shared agenda is not only strong but already producing results for New Yorkers,” he said in a statement.