A federal judge approved a plan by General Motors late on Sunday to sell its best assets to a new, government-backed company, a crucial step for the automaker to restructure and complete its trip through bankruptcy court.

The decision by the judge, Robert E. Gerber of United States Bankruptcy Court in Manhattan, came after three days of hearings to address the 850 objections to the restructuring plan and after he had received a revised sale order from G.M.’s lawyers.

In his 95-page opinion, Judge Gerber wrote that he agreed with G.M.’s main contention: that the asset sale was needed to preserve its business in the face of steep losses and government financing that is scheduled to run out by the end of the week.

“Bankruptcy courts have the power to authorize sales of assets at a time when there still is value to preserve — to prevent the death of the patient on the operating table,” Judge Gerber wrote.

With the approval of the restructuring plan, G.M. and the government are seeking to close the sale by Thursday afternoon, when a four-day stay of the judge’s order expires. The government, which is financing the reorganization, had given G.M. until Friday to win approval for the sale or risk losing its bankruptcy financing.

Harry J. Wilson, a member of the Obama administration’s auto task force, testified on Wednesday that the administration did not intend to extend the loan by even one day beyond the deadline.

Judge Gerber’s approval marks yet another victory for the Obama administration, which has sought an enormous restructuring of the American auto industry in an extraordinarily short time span. Last month, a new Chrysler emerged from bankruptcy in just 42 days despite a challenge by three Indiana state funds that went as high as the Supreme Court.

If completed by Friday, G.M. would be near the end of an unusually quick trip through the bankruptcy courts, turning itself into smaller company with fewer brands and a new focus on fuel-efficient cars.

Under the terms of the revised deal, G.M. would sell its most desirable assets, including the Chevrolet and Cadillac brands, to a new company owned largely by the American and Canadian governments and a health care trust for the United Automobile Workers union. The Obama administration anticipates taking the company, which will still bear the General Motors name, public next year.

G.M.’s chief executive of three months, Fritz Henderson, is expected to hold that position in the new company. The Obama administration has already designated several directors for the new G.M., including Edward Whitacre, AT&T’s former chief executive, as chairman. The company will be represented on an interim basis by Cadwalader, Wickersham & Taft, the law firm that advised the auto task force.

Old G.M. will stay in bankruptcy, overseen by the company’s current chief restructuring officer, Albert A. Koch of the turnaround firm AlixPartners. The Obama administration has agreed to provide $1.175 billion while the company winds down its estate and settles claims.

Along the way, the company has shed 21,000 union workers and closed 12 to 20 factories. In addition, 40 percent of G.M.’s 6,000 dealers will close.

It is possible that creditors who objected to the terms could file an appeal. Lawyers for several opponents argued during the hearings that the G.M. sale stripped them of their rights as creditors. A lawyer representing three dissident bondholders urged Judge Gerber to call what he said was the Obama administration’s bluff on the July 10 deadline.

The lawyer, Michael Richman of Patton Boggs, and others said that while they were not opposed to a sale, they objected to the plan’s structure and said they deserved more compensation for their claims. Mr. Richman’s clients hold $2.3 million of G.M.’s $27 billion in bonds, though they assert they represent a wider group of individual bondholders that owns more than $400 million worth of bonds.

Other groups, including those representing product liability claims and asbestos litigants, also fought against G.M.’s plan. Under the terms of the sale, most of those claims would remain with the remnants of G.M. in bankruptcy, meaning they were likely to recover little, if anything.

But G.M.’s chief bankruptcy counsel, Harvey R. Miller, said Thursday that none of the 850 objectors to the sale of assets presented a credible alternative. The only other option would be liquidation, a process that he said would benefit no one.