The race to lead New York City has tightened since Mayor Eric Adams exited the contest, but Zohran Mamdani, the Democratic nominee, maintains a 13-point lead a month before Election Day, according to a new poll released on Thursday.

The survey, conducted by Quinnipiac University, offered the first detailed snapshot since Mr. Adams’s decision to end his flagging campaign in late September.

It indicated that most of the mayor’s support transferred to former Gov. Andrew M. Cuomo, improving his standing from September, when the pollster found him trailing by 22 points in a four-way contest.

Overall, 46 percent of likely voters now say they plan to vote for Mr. Mamdani, compared with 33 percent for Mr. Cuomo, who is running on a third-party ballot line after losing the Democratic primary in June. About 15 percent of likely voters support Curtis Sliwa, the Republican nominee.

“The numbers changed,” said Mary Snow, the group’s assistant director. “But the contours of the race haven’t.”

The poll, conducted Oct. 3 through Oct. 7, offered Mr. Mamdani and Mr. Cuomo cause for both optimism and concern. It had a margin of error of 3.9 percentage points.