BUENOS AIRES--Argentina's negotiating team is set to return home Friday after a meeting earlier in the day with a court-appointed mediator in New York failed to resolve a high-stakes dispute over unpaid debts that could see the country default as early as next week.

Argentine officials briefly met alone Friday morning with the mediator, Daniel Pollack, who said they would return to Buenos Aires to seek instructions from their government. Mr. Pollack said he later spoke by telephone with representatives of the hedge funds that have sued Argentina to collect on debt it stopped paying 13 years ago.

"No resolution of the impasse between the parties has been reached," Mr. Pollack's office said in a statement. "I anticipate that there will be further communications with the parties prior to the default date."

Argentina's Economy Ministry said in a statement it expects talks with Mr. Pollack to continue in coming days. A spokesman for Elliott Management Corp. affiliate NML Capital Ltd. declined to comment.

Argentina's benchmark Merval stock index was down 2.1% in afternoon trading, led by declines in shares of state oil company YPF SA and banking concern Grupo Financiero Galicia SA. The 2033 discount bond fell 3.3%, to 1,190 pesos ($145).

Argentina has largely run out of legal options after the U.S. Supreme Court on June 16 declined to hear its appeal in the case. That left in place U.S. District Judge Thomas Griesa's ruling that Argentina has to pay the hedge funds when it pays investors who own bonds the country issued in debt restructurings following the 2001 default.

Judge Griesa blocked interest payments for $539 million on some of those bonds after Argentina deposited the funds with the bond trustee last month, but didn't pay the hedge funds. Argentina has until Wednesday to get that money to bondholders or run the risk defaulting.

Earlier this week, the judge told Argentina and hedge funds to meet "continuously" with Mr. Pollack to reach a deal ahead of next week's payment deadline.

President Cristina Kirchner's government has argued that paying the hedge funds the $1.6 billion they have won in U.S. courts could bankrupt the country by triggering more than $120 billion in claims by other holdout creditors and investors who own restructured bonds.

The administration says a major hurdle to negotiating a settlement now is a clause in the restructured bonds that allows investors to demand the same treatment if Argentina cuts a better deal with holdouts.

Argentina wants Judge Griesa to suspend his ruling until after the clause expires at the end of this year so the country can keep paying its bonds while it seeks a resolution to the creditor dispute, Mrs. Kirchner's cabinet chief, Jorge Capitanich, told reporters Friday morning.

Argentina's battle with the hedge funds stems from its default on some $100 billion in debt in 2001. The country offered holders of the defaulted bonds new securities valued at about 33 cents on the dollar in 2005 and 2010.

Between the two swaps, investors agreed to exchange almost 93% of defaulted bonds eligible for restructuring. However, hedge funds led by NML Capital and Aurelius Capital Management LP declined to accept the offer and instead sued for full repayment.

Shane Romig contributed to this article

Write to Ken Parks at ken.parks@wsj.com

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