The Senate on Thursday overwhelmingly confirmed Gen. Randy George of the Army and Gen. Eric Smith of the Marines as the chiefs of staff of their respective services, circumventing a single senator’s blockade against senior military promotions but leaving hundreds more still in limbo.

The action followed the confirmation on Wednesday night of Gen. Charles Q. Brown Jr. to serve as the next chairman of the Joint Chiefs of Staff. The three moved forward after Senator Chuck Schumer, Democrat of New York and the majority leader, steered around a longstanding roadblock by Senator Tommy Tuberville, Republican of Alabama, who has halted military promotions in protest of a Pentagon policy on abortion access.

But Mr. Tuberville made it clear that he had no intention of lifting his blockade unless the Defense Department reversed its policy, which provides time off and travel reimbursement to service members needing to go long distances to obtain abortions or other forms of reproductive health care.

If anything, the confirmations seemed only to embolden Mr. Tuberville, as Mr. Schumer had long said he feared they might. The Alabama senator said the only way to get around his obstruction would be for Mr. Schumer to continue to consider the promotions one by one, a time-consuming process that Democrats and many Republicans agree is untenable.

The developments have prompted a backlash from some Democrats, who are frustrated that Republicans have been able to hold up a large number of promotions to try to force a policy change.

“In my mind, you need to change the rules so that you can’t have blanket holds anymore,” said Senator Jeanne Shaheen, Democrat of New Hampshire. “I don’t think we ought to have blanket holds on military, general nominees.”

But Republicans said they hoped the approval of three senior generals would help end the standoff.

“When you’re working on a big, difficult issue, if you can show a little bit of progress, sometimes that can spur action to solve the broader problem,” said Senator Dan Sullivan, Republican of Alaska. “I think this little breakthrough helped.”

Mr. Sullivan has been one of the chief Republican figures pushing to put individual military promotions on the floor, as a means of filling vacancies without forcing Mr. Tuberville to end his protest.

But he is also working with senior Democratic senators like Jack Reed of Rhode Island, the chairman of the Armed Services Committee, to negotiate a deal to lift the blockade. In an interview on Thursday, he suggested that Mr. Tuberville might stop blocking one- and two-star generals if the Senate continued to confirm high-profile nominees like Generals Brown, George and Smith, as part of a negotiated compromise. He would not say whether such a deal would have to include a change to the Pentagon’s policy, which Mr. Tuberville has demanded, and Democrats have rejected.

It is also unclear what the Democrats and Republicans who believe Mr. Tuberville’s protest is wrong would be willing to accept as part of a negotiated deal. Mr. Schumer has not said whether he would be willing to use similar maneuvers to advance additional high-profile military promotions. And Mr. Reed said he was concerned about accommodating Mr. Tuberville’s protest more than the Senate already has.

“We’re in the process, if we go forward much further than this, of politicizing the military,” Mr. Reed said. “They now become bargaining chips in policy wars which they have nothing to do about.”