Clayton Fuller will face Shawn Harris, a Democrat, in an April runoff. Mr. Fuller’s win over a flashier Republican showed the power of the president’s support.

Through his lawyers, Alberto Carvalho, who was put on leave after the F.B.I. raided his home and office, said that his actions were appropriate but that he would respect the investigative process.

Two doctors affiliated with the university and NewYork-Presbyterian Hospital stepped down after an external report found that the administrators mishandled allegations of abuse against Robert Hadden.