Ever since the Trump administration announced last month that it would review the Smithsonian’s exhibitions and seek changes to programming it found objectionable, historians and curators have been wondering how the historically independent institution would respond.

The Smithsonian offered the first indication on Wednesday afternoon when Lonnie G. Bunch III, the Smithsonian’s secretary, sent a letter to the staff indicating that the institution had agreed to set up a team to review turning over materials to the White House, as requested, but to do so as an autonomous institution.

“I take my responsibility to steward the institution on behalf of the American people very seriously,” the letter to staff said, adding, “Our independence is paramount.”

In a letter to Mr. Bunch last month, the administration told the Smithsonian to submit information about programming at eight of its 21 museums within a 75-day deadline, and that the White House would then direct possible changes in content.

While complimenting Mr. Trump’s “admiration and regard for the Smithsonian,” Mr. Bunch told the staff that his response to the White House, sent in a letter on Tuesday, had reiterated the institution’s intention to rigorously review its content for inappropriate partisanship. But he said it would be the Smithsonian, not the executive branch, that would direct the effort.

“Our own review of content to ensure our programming is nonpartisan and factual is ongoing, and it is consistent with our authority over our programming and content,” Mr. Bunch wrote in his letter to the staff.