General Motors Corp. outlined a new turnaround plan that would leave the U.S. government controlling the auto maker, as it set up a showdown with bondholders that could determine whether the company lands in bankruptcy court.

Under the plan, GM is asking the Treasury Department for an additional $11.6 billion in loans, on top of the $15.4 billion it has already received. It envisions giving the government at least half ownership of the company as payment for half of the loans.

At...