Participants in the meetings were expected to include Christopher A. Wray, the F.B.I. director; Rod J. Rosenstein, the deputy attorney general; and Dan Coats, the director of national intelligence, along with other F.B.I. and Justice Department officials.

John F. Kelly, the White House chief of staff, was also scheduled to attend — a decision that was sure to rankle Democrats who have warned that it is inappropriate for a member of the White House staff to be present to learn about delicate investigative files related to an inquiry involving the president. The White House said on Tuesday that no White House staff members would attend.

Mr. Kelly had agreed to arrange the meeting amid the rancor between senior law enforcement officials and Republican congressmen loyal to the president, including Representative Devin Nunes of California, the chairman of the House Intelligence Committee.

Representative Trey Gowdy, Republican of South Carolina, was also invited to attend both meetings, even though he is not a member of the Gang of Eight. Mr. Gowdy, a former federal prosecutor, has been brought into several meetings between Mr. Nunes and the Justice Department to help lower tensions.

The arrangement was a victory for the senators and for Democrats, who publicly urged the Justice Department and the F.B.I. to reconsider holding the meeting with Mr. Nunes. Senator Chuck Schumer of New York, the Democratic leader, pressed Mr. McConnell throughout the day on Wednesday to demand access for the Gang of Eight.

“This meeting is completely improper in its proposed form and would set a damaging precedent for your institutions and the rule of law,” Mr. Schumer and Representative Nancy Pelosi of California, the House Democratic leader, wrote in a joint letter earlier in the day. “We can think of no legitimate oversight justification for the ex parte dissemination — at the direction of the president — of investigative information to the president’s staunchest defenders in Congress and, ultimately, to the president’s legal defense team.”

The inclusion of the Gang of Eight could serve to blunt Mr. Nunes’s continued attacks on the Justice Department.