Kim Sajet, the director of the National Portrait Gallery whom President Trump announced he was firing last month, is stepping down, explaining in a statement that she thought her decision was in the best interests of the institution.

This week the Smithsonian, which oversees the museum and has long operated as independent of the executive branch, reiterated that it retains the legal authority over personnel including Ms. Sajet, whom the president had criticized as partisan. But the institution also said it was committed to presenting its scholarship “free from political or partisan influence.”

Ms. Sajet did not discuss the president or his remarks in her statement, which was included in an email sent to the staff by Lonnie G. Bunch III, the Smithsonian’s secretary.

“This was not an easy decision, but I believe it is the right one,” she said. “From the very beginning, my guiding principle has been to put the museum first. Today, I believe that stepping aside is the best way to serve the institution I hold so deeply in my heart.”

In his email, Mr. Bunch said: “We thank Kim for her service. She put the needs of the Institution above her own, and for that we thank her.”

He added that Kevin Gover, the Smithsonian’s under secretary for museums and culture, will serve as the National Portrait Gallery’s acting director.