The House Judiciary Committee has issued subpoenas for James B. Comey, the former F.B.I. director, and Loretta E. Lynch, the former attorney general, as part of an investigation into their handling of inquiries into Hillary Clinton’s email server and possible ties between the Trump campaign and Russia.

The subpoenas, issued on Wednesday by Representative Robert W. Goodlatte of Virginia, the committee’s chairman and a Republican, require Mr. Comey and Ms. Lynch to appear in closed-door sessions with members of Mr. Goodlatte’s committee and the Oversight and Government Reform Committee. Mr. Comey has been called to appear on Dec. 3, and Ms. Lynch a day later.

On Twitter, Mr. Comey objected to the format that Republicans are demanding for the interview. “I’m still happy to sit in the light and answer all questions,” he said. “But I will resist a ‘closed door’ thing because I’ve seen enough of their selective leaking and distortion. Let’s have a hearing and invite everyone to see.”

Several Republicans have said they believe that Mr. Comey and Ms. Lynch were part of a deeply rooted bias within the F.B.I. and the Justice Department that allowed Ms. Clinton to escape prosecution for her use of a private email server during her time as secretary of state. The Republicans have also alleged impropriety in the origins of the investigation into the Trump campaign’s connections to Russia.