Although he has yet to pick a schools chancellor, Mr. de Blasio has made a number of other top appointments, including his first deputy mayor, Anthony E. Shorris; his police commissioner, William J. Bratton; and his budget director, Dean Fuleihan.

Like Ms. Carrión, all have long records of government service, in some cases going back to the last two Democratic mayoral administrations. Asked on Sunday where Republicans might fit into his plans, Mr. de Blasio, who has promised to assemble a team “that mirrors the glorious diversity of this city,” at first made light of such bipartisanship.

“Let’s not get crazy about this diversity idea,” he said, laughing.

Mr. de Blasio then turned more serious. He described how inclusivity could be reimagined at his City Hall and said his team so far had people from the Koch, Dinkins, Giuliani and Bloomberg administrations.

“You know what?” he said. “It’s a free country. We consider Republicans, too, but they have to share our values. That might be a high bar for some Republicans.”

As for child welfare, Mr. de Blasio said it was a mission he was committed to and had focused on for years. He said that the agency was charged “literally with some of the most important work the government does,” but that gaps still existed.

Ms. Carrión now finds herself preparing to lead an agency that had faced considerable criticism over the years and was the subject of renewed scrutiny after the death in 2010 of Marchella Pierce, a 4-year-old girl who was drugged, beaten and tied to a bed by her mother and grandmother, even as the family was under the supervision of the agency. Last week, two former employees of the agency pleaded guilty to misdemeanor charges relating to the Marchella’s death.

The employees, Damon T. Adams, a caseworker with the agency, and Chereece M. Bell, a supervisor, reached an agreement with prosecutors after initially being indicted on charges of criminally negligent homicide, a felony. The case led the Brooklyn district attorney, Charles J. Hynes, to start a grand jury investigation into “evidence of alleged systemic failures” at the agency.