Mayor Bill de Blasio’s approval rating has ticked up amid his concerted effort to convey a more forceful public image, and he now receives positive marks from half of New York City voters, a Quinnipiac University poll released on Tuesday found.

But support for Mr. de Blasio, who garnered a 50 percent job approval rating, remains polarized along racial lines, and voters are split on whether he deserves to win a second term in 2017. Black and Hispanic voters approve of the mayor by large margins, but two-thirds of whites disapprove.

A modest plurality of voters said Mr. de Blasio, who is a Democrat, deserved to win a second term. Forty-eight percent said he should be re-elected; 44 percent said he should not.

The poll would seem to allay fears, at least for now, that Mr. de Blasio’s political position might deteriorate precipitously, buckling under persistent criticism of his management style and his response to a spike in homelessness. An Oct. 29 poll by Quinnipiac showed him with a 45 percent approval rating.