They also wanted to ask Mr. Priebus about a 2016 meeting between Trump campaign officials — including Mr. Trump’s son Donald Trump Jr. and his campaign chairman at the time, Paul Manafort — and Russians who promised derogatory information on Hillary Clinton, the Democratic presidential nominee. Mr. Manafort had been scheduled to meet with Mr. Priebus on the day of the June 9, 2016, meeting.

Mr. Priebus was scheduled to be interviewed in recent weeks. But it was repeatedly delayed because Mr. Mueller’s office had not yet received all of the documents it had requested from the White House related to the matters about which investigators wanted to question Mr. Priebus.

Investigators are expected to interview several other current and former White House officials in the coming days, including Mr. Trump’s former White House spokesman, Sean Spicer, and the White House communications director, Hope Hicks.

Mr. Mueller wants to question Mr. Spicer and Ms. Hicks about what occurred on an Air Force One flight in July, when Mr. Trump and his advisers deliberated about how to respond to questions from the news media about the June 2016 meeting between the campaign officials and the Russians.

The first statement released about the June 2016 meeting said it was primarily about adoption issues, neglecting to mention that it was arranged under the premise that the Russians would provide the Trump campaign with derogatory information on Mrs. Clinton.