Nearing the end of his first year in office, Mayor Bill de Blasio is receiving waning, if still fairly robust, support from New Yorkers, with a sharp racial divide over his performance, according to a poll released on Tuesday.

Forty-nine percent of voters approved of the mayor’s handling of his job, compared with 36 percent who disapproved, according to the survey, by Quinnipiac University. Less than three months ago, 50 percent approved of the mayor’s work and 32 percent disapproved.

Since August, Mr. de Blasio, a Democrat in an overwhelmingly Democratic city, has improved upon already impressive reviews from black voters, with support rising to 71 percent, from 65 percent in the last poll. The mayor also won praise from Hispanic voters, with 56 percent approving and 27 percent disapproving, the new poll said.

But among white voters, the mayor’s approval rating has slipped to 34 percent, with 50 percent disapproving of his performance. In August, 36 percent of white voters approved, and 45 percent disapproved.