Mr. de Blasio has encountered a series of difficulties in recent months, including the tussle with Mr. Cuomo, also a Democrat, over a disappointing legislative session in Albany, and distressing headlines about a rising murder rate — even as city officials have noted that overall crime continues to fall.

The mayor was also recently the subject of negative ads from the car-hailing company Uber, which opposed a proposed cap on its growth that the mayor had promoted. (The city has, for now, backed away from the proposal.)

Administration officials were quick to connect the increase in disapproving voters — a four-point uptick since May — to the Uber campaign, noting that the mayor’s numbers also suffered for a time last year during a public dispute with advocates of charter schools.

“This is a mayor who focuses on the fundamentals New Yorkers care about, not political chatter,” a spokesman, Wiley Norvell, said in a statement, citing crime reductions and the city’s housing plans.

Aides also highlighted unfavorable polls for Michael R. Bloomberg at a similar point in his first term as mayor. In July 2003, 31 percent of voters approved of his stewardship of the city; 60 percent disapproved. (At the time, Mr. Bloomberg, a Republican who later became a political independent, had drawn the ire of many voters for championing antismoking legislation and for deciding to raise property taxes.)