WASHINGTON — Mike Pompeo came close on Thursday to clinching confirmation as the nation’s 70th secretary of state when Senator Heidi Heitkamp, Democrat of North Dakota, announced her support. But before that triumph, he is expected to face a historic rebuke from the Senate Foreign Relations Committee, which most likely will not recommend his confirmation.

Ms. Heitkamp, who faces a difficult re-election fight in a state that President Trump won handily, said in a statement that Mr. Pompeo had convinced her that he would rebuild the State Department, which was seriously depleted under the previous secretary of state, Rex W. Tillerson.

“At a time of peril around the world, we need to exhaust all diplomatic options before sending the brave men and women of the armed forces into dangerous situations that could escalate out of control,” she said.

Ms. Heitkamp’s announcement is likely to push other moderate Democrats facing re-election in states that Mr. Trump won to follow suit. Many of those senators — including Joe Manchin III of West Virginia and Claire McCaskill of Missouri — voted for Mr. Pompeo last year when he was confirmed to be C.I.A. director, and they are under renewed pressure at home to show they are willing to vote with Mr. Trump’s interests from time to time.