Mr. Johnson’s more assertive posture is reflective of an attitude shared by many Council members, including those who ran against Mr. Johnson for speaker and others who did not support his bid.

Councilman Benjamin Kallos of Manhattan welcomed a new era of debate. “I think conflict is good for resolving problems,” he said.

“The notion that the mayor is the sole branch of New York City government is an anachronism,” said Ritchie Torres, a councilman who represents the Bronx. “It has no place in the age of Corey Johnson.”