The bondholders of General Motors ( GM) plan to present a counteroffer Thursday to the automaker's debt swap that will seek a majority stake in GM, published reports say.

The bondholder committee, which represents about 20% of the debt outstanding, proposes that GM issue new stock and give 51% of the reorganized company to the bondholders, a 41% stake to the United Auto Workers union and 1% to common equity holders, reports the Wall Street Journal.

The bondholder committee plans to reject GM's debt exchange offer made earlier this week that asked them to swap all their claims for a 10% stake in a reorganized company, Bloomberg reports, citing a person familiar with the committee representing creditors.

The U.S. government wouldn't get equity under the bondholders' counterproposal because it wouldn't need to reduce any of GM's loans. Unsecured bondholders would likely reduce their entire claim on the automaker under the plan, according to the Journal.

The counterproposal could meet stiff resistance from the Obama administration's automotive task force, as administration officials have said the GM deal as proposed is more than fair, and have told bondholders they would likely see less under bankruptcy, the Journal notes.

GM is hurrying to complete the debt-for-equity exchange and other deals by a June 1 deadline in an effort to stay out of bankruptcy court.

Treasury officials have told GM that 90% of the company's bondholders must participate in the exchange, the Journal reports.