WASHINGTON — The new acting director of national intelligence, Richard Grenell, has asked an intelligence official who angered some lawmakers with a briefing about Russian interference in the 2020 election to stay on in her role.

Mr. Grenell’s move is a peace offering to the 17 intelligence agencies he oversees and a potential sign that he will not be conducting a widespread purge, as some administration officials have feared. Mr. Grenell, a Trump loyalist who has little experience in intelligence, removed the No. 2 official in his office in his first day on the job last week.

Whether Mr. Grenell, appointed to the post last week by President Trump, can win over members of Congress and the intelligence community will depend in part whether he can convince them that he will focus on protecting the elections from outside interference.

Some administration officials feared that the official who briefed the lawmakers, Shelby Pierson, would be removed as well. As the intelligence community’s top election security official since last year, she was subjected to withering criticism after her briefing to a classified hearing of the House Intelligence Committee on Feb. 13 touched off a fierce partisan debate over the nature of Russia’s interference in the 2020 election.