WASHINGTON — The threat of a federal government shutdown ended late Saturday, hours before a midnight deadline, as Congress approved a temporary funding bill to keep agencies open and sent the measure to President Biden to sign.

The rushed package drops aid to Ukraine, a White House priority opposed by a growing number of GOP lawmakers, but increases federal disaster assistance by $16 billion, meeting Biden’s full request. The bill funds government until November 17.

After whirlwind days of turmoil in the House, Speaker McCarthy suddenly abandoned demands for steep spending cuts from his right flank and instead relied on Democrats to pass the bill, at risk to his own job. The Senate followed with final passage.

“We’re going to do our job,” Mr. McCarthy said before the House vote. “We’re going to be adults in the room. And we’re going to keep government open.”

It’s been a head-spinning turn of events in Congress after days of House chaos pushed the government to the brink of a disruptive federal shutdown.

The outcome ends, for now, the threat of a shutdown. If no deal had been in place before 12:01 A.M. Sunday, federal workers would have faced furloughs, more than 2 million active-duty and reserve military troops would have had to work without pay and programs and services that Americans rely on from coast to coast would have begun to face shutdown disruptions.

“Americans can breathe a sigh of relief,” said Senator Schumer.

The package funds government at current 2023 levels until mid-November, setting up another potential crisis if they fail to more fully fund government by then. The package was approved by the House 335-91, with most Republicans and almost all Democrats supporting. Senate passage came by an 88-9 vote.

Yet the loss of Ukraine aid was disappointing for lawmakers of both parties vowing to support President Zelensky after his recent Washington visit. The Senate bill included $6 billion for Ukraine, and both chambers came to a standstill Saturday as lawmakers assessed their options.

“The American people deserve better,” said the House Democratic leader, Congressman Hakeem Jeffries of New York, warning in a lengthy floor speech that “extreme” Republicans were risking a shutdown.

For the House package to be approved, Mr. McCarthy was forced to rely on Democrats because the speaker’s conservative flank has said it will oppose any short-term funding measure, denying him the votes needed from his slim majority. It’s a move that risks his job amid calls for his ouster.

After leaving his right-flank behind, Mr. McCarthy is almost certain to face a motion to try to remove from office, though it is not at all certain there would be enough votes to topple the speaker.

Most House Republicans voted for the package Saturday while 90 opposed.