US judge Thomas Griesa, who is seeking to settle a long-drawn dispute between Argentina and the holdout creditors who did not take part in the country's debt restructuring in 2002, ordered the parties to meet with a court-appointed mediator "continuously until a settlement is reached.
The order comes as time is running out for Argentina to avoid a fresh default.
"That is about the worst thing I can envision. I don't want that to happen," Reuters quoted Griesa as saying.
Meanwhile, Jonathan Blackman, a lawyer representing Argentina, said a deal would be "unlikely, if not impossible" even with around-the-clock talks.
"It simply can't be done by the end of the month," he said.
Griesa appointed Daniel Pollack as a mediator between the parties on 23 June. Despite multiple talks, the parties are yet to reach an agreement. Another meeting is scheduled on 23 July.
Argentina has been engaged in a long legal battle with hedge funds led by Elliott Management and Aurelius, which refused to take part in the country's debt restructuring. About 92% of the country's creditors agreed to swap debts and accept less money.
In a major blow to the government, Griesa earlier gave a ruling that bars Argentina from paying the holders of its restructured debt unless it pays the hedge funds.
Following the adverse order from Griesa, Argentina claimed that if the country paid the suitors on their terms, it would lead to claims from other holdouts of around $15bn (£8.8bn, €11bn) in debt.
The government's coupon payment to restructured bondholders through a New York bank had earlier been blocked by Griesa. As a result, the country is facing a technical default by the end of July if it does not make a settlement with the so-called "vulture funds".
Despite the bitter spat with them, Argentina will have to settle with the holdout funds as it has few alternatives to avert a default, which would damage its reputation further in the international capital market.