House Republicans plan to privately question the deputy attorney general, Rod J. Rosenstein, about discussions last year where he suggested secretly taping President Trump to expose a chaotic White House and removing him from office under the 25th Amendment.

Mr. Rosenstein and Representative Robert W. Goodlatte, Republican of Virginia and chairman of the House Judiciary Committee, spoke Thursday night and agreed to schedule a meeting in the coming weeks, Mr. Goodlatte said in a statement.

“There are many questions we have for Mr. Rosenstein, including questions about allegations made against him in a recent news article,” Mr. Goodlatte said, referring to the New York Times article last week that revealed Mr. Rosenstein’s discussions with other law enforcement officials. “We need to get to the bottom of these very serious claims.”

House Democrats complained that they were left out of the planning and pledged to push to attend the meeting. Representative Jerrold Nadler of New York, the top Democrat on the House Judiciary Committee, said his Republican colleagues “cannot be left alone in a room” with Mr. Rosenstein.