House Republicans took a critical step late Thursday night toward bringing up the long-stalled foreign aid bill for Ukraine and Israel, after being forced to rely on Democratic votes to move a plan to consider it out of a key committee and onto the floor.

The 9-to-3 vote in the critical Rules Committee was an early step in the convoluted process the House is expected to go through over the next couple of days to approve the $95 billion aid package. It reflected the extent of far-right anger over Speaker Mike Johnson’s plan to push through the legislation over the opposition of ultraconservative Republicans, and underscored how heavily the speaker will have to rely on Democrats to push it across the finish line.

In a spasm of anger, three far-right Republicans on the panel, which controls what legislation comes to the House floor, refused to back the rule needed to bring up the foreign aid bill, putting it on track to die in committee. But Democrats on the panel stepped in to save it in an extraordinary breach of custom.

All Democrats voted to advance the plan out of committee.

The Rules Committee has traditionally been an organ of the speaker, and legislation is typically advanced to the floor in a straight party-line vote.

Democrats will all but certainly have to provide the votes on the House floor to approve the rule and allow the aid package to be brought up, lending their support in an yet another unorthodox vote in the face of Republican opposition.

The rule is critical to Mr. Johnson’s plan for pushing the foreign aid package through the House, because it would allow separate votes on aid to Israel and aid to Ukraine, which are supported by different coalitions, but then would fold them together without requiring lawmakers ever to cast an up-or-down vote on the entire bill.

The group of far-right lawmakers who sought to block the measure in committee won their seats on the Rules panel as part of a concession made last year by the speaker at the time, Kevin McCarthy, who had to haggle with ultraconservatives who opposed electing him to the top post and agreed to back him only after he granted them critical leverage. They refused to support the measure to bring up the foreign aid package because it would not allow a vote on severe border security provisions they have said should be prioritized over aiding Ukraine.

That amounted to a remarkable act of rebellion, and left Democrats to bail out the speaker and push the measure through the panel.

Mr. Johnson earlier said he expected a House vote to pass the aid package on Saturday.

“I’d rather send bullets to Ukraine than American boys,” he said in an interview on Newsmax on Thursday night. “We don’t want to have boots on the ground, and we can prevent that by allowing them to hold Putin at bay.”