Adams has stressed that he plans to focus on rooting out inefficiency and he has several proposals he wants to introduce but the scope of the fiscal challenges will likely require making difficult choices.

He has made it clear that big business has a role to play in shepherding the city’s recovery, and there are indications that he may have a far warmer relationship with business leaders than Mr. de Blasio, who was elected on a fiery populist platform.

“He’s restored confidence that the city is a place where business can thrive,” said Kathryn S. Wylde, who leads the business-aligned Partnership for New York City. “He’s demonstrated that he has the courage to, basically, be politically incorrect when it comes to dealing with the demonization of wealth and business.”

In New York City, even as Republicans appeared poised for the possibility of slight gains in the City Council, Democrats won the marquee contests easily. It seemed likely that many of the officials Mr. Adams must work with closely prominent incoming City Council members, the public advocate and other Democrats who won on Tuesday will be substantially to Mr. Adams’s left.

Adams, whose win over his Republican opponent, Curtis Sliwa, appeared to be resounding, will begin the job with significant political leverage.