The group, led by Paul E. Singer’s NML Capital, appealed on Friday to Judge Thomas P. Griesa of the Federal District Court in Manhattan to allow Citigroup to make a $5 million payment to bondholders by a Tuesday deadline.

After more than two hours of debate, Judge Griesa agreed to a temporary stay on his previous order that had blocked the payment. He also called for another hearing in 30 days to consider arguments from Citigroup that its activities related to the Argentine bonds were exempt from his rulings.

“We do not want to be here over and over again,” Judge Griesa added, referring to what has become an increasingly messy case.

One of the judge’s earlier rulings in favor of the hedge funds had blocked Citigroup’s Argentina branch from making the payment. Citigroup then made a plea to the United States Court of Appeals for the Second Circuit to reconsider the decision, saying that it faced “grave sanctions” from Argentina and that the country was holding a gun to its head. The appeals court rejected the case, however, and sent it back to Judge Griesa’s court.

The stay will allow Judge Griesa time to consider new evidence submitted by Citigroup, which has sought to establish that his order should not apply to it.

The stay is the latest development in a battle that has been going on for years between Argentina and the hedge funds, which are seeking a $1.5 billion payment on bonds that Argentina defaulted on in 2001.

Argentina has refused to pay the so-called holdout hedge funds, which own bonds that were withheld from two restructurings that exchanged defaulted bonds for discounted ones.

But in a victory for the holdout hedge funds, Judge Griesa ruled that Argentina could no longer pay its restructured bondholders without also paying the holdout hedge funds. The decision led to Argentina’s second default in barely more than a decade in July.

The ruling has begun to embroil several financial institutions and bondholders on the sidelines. Argentina has defied the order by depositing interest payments for its restructured bonds with Citigroup and with the Bank of New York Mellon, which so far have not passed them on to bondholders.

This has placed the two banks in a difficult position: If they pass on the money from Argentina to bondholders, they will defy Judge Griesa’s order. But if they do not, they face severe penalties from Argentina.

In an attempt to extricate itself from the bigger battle, Citigroup has argued that the payments it has received are for bonds governed by Argentine law, not by New York law, and thus are not covered by Judge Griesa’s injunction.

Karen Wagner, a lawyer for Citigroup, said on Friday that the hedge funds “are not entitled to have an injunction hanging over Citibank’s head.”

Lawyers for the holdout hedge funds, meanwhile, contend that exempting Citigroup from Judge Griesa’s injunction would “open the floodgates for others to request carve-outs, killing the injunction by a thousand cuts and straining the court’s resources.” But they argued for the stay on Friday because it gives them time to counter Citigroup’s arguments.

Separately, Judge Griesa will hold another hearing on Monday to determine whether Argentina is in contempt of court.