The court will hold a private conference on Sept. 30 to decide whether to consider an appeal by Argentina of a ruling in favor of the creditors in October by the Second United States Circuit Court of Appeals. The Supreme Court could reach a decision as soon as Oct. 1.

The group of creditors, known as holdouts because they have refused to accept anything other than full repayment, includes Elliott Management, a hedge fund run by the billionaire Paul E. Singer, and Aurelius Capital Management.

Their case goes back to 2001, when Argentina defaulted on close to $100 billion in loans. Since then, the government has twice negotiated deals with the majority of bondholders to exchange the original debt for new “exchange” bonds worth a lot less.

The holdouts rejected these new bonds and instead have sued the Argentine government, arguing that the government is now capable of making full repayments. They have demanded to be paid more than $1.33 billion.

On Aug. 23, a three-judge panel of the United States Court of Appeals for the Second Circuit in New York upheld the lower court decision.

If the Supreme Court chooses not to consider the appeal, the Argentine government will be one step closer to paying the creditors in full.

Legal specialists have said that a final ruling in favor of the creditors could send waves across the international debt market used by countries to help finance their governments.

The case has pitted the creditors against Argentina’s president, Cristina Fernández de Kirchner, who has accused the holdout group of creditors of being “vultures.”

To help the group’s image, Mr. Singer joined the lobbying group American Task Force Argentina in bringing a small group of Argentine pensioners who are part of the holdout group to New York in January.

“There has been an enormous amount of gamesmanship of disproportion,” Anna Gelpern, a senior fellow at the Peterson Institute for International Economics, said in response to the back and forth between the holdouts and Mrs. Kirchner.