WASHINGTON — Christopher A. Wray was the government’s top criminal prosecutor in 2004 when the F.B.I. director, Robert S. Mueller III, and the deputy attorney general, James B. Comey, threatened to quit the Bush administration over a controversial surveillance program. He offered to join their protest.

Now, with President Trump’s selection of Mr. Wray on Wednesday to be the director of the F.B.I., all three men will be central figures in the investigation of Russian meddling in the 2016 election that has rocked the Trump administration. Mr. Mueller is leading the investigation into Russian influence — and the inquiry led Mr. Trump to fire Mr. Comey.

In choosing Mr. Wray, the president is calling on a veteran Washington lawyer who is more low key and deliberative than either Mr. Mueller or Mr. Comey but will remain independent, friends and former colleagues say.

“He’s not flashy. He’s not showy. He’s understated,” said J. Michael Luttig, a former judge who hired Mr. Wray as a law clerk in 1992. Mr. Luttig, who said he counted Mr. Comey and Mr. Mueller as friends, said Mr. Wray would bring a more subtle management style to the F.B.I.