A stalemate involving the creditors and Argentina’s last president, Cristina Fernández de Kirchner, led the country to default on its debt again in 2014. The new administration of President Mauricio Macri has indicated that it wants to resolve the debt as part of a bigger move to reform Argentina’s economy.

Luis Caputo, the newly appointed finance secretary, and other senior government representatives met this week with principals at the hedge funds — including Mr. Elliott’s NML Capital unit, Aurelius Capital, Montreux Partners, Dart Management and Davidson Kempner — in Manhattan, according to a court-appointed arbiter Daniel A. Pollack. The group is seeking a resolution for claims totaling around $9 billion, he added.

In dispute is how much Argentina should pay in interest.

At a news conference in Buenos Aires announcing the deal with Italian bondholders, Argentina’s economic minister, Alfonso Prat-Gay, touched on the question of interest payments. “We have said that we will respect the bond principal and that we are going to be firm in negotiating the interest, and in this particular agreement we have achieved just that.”

But, Mr. Prat-Gay added, “The difficulty that we have right now is that some bondholders want to be paid an interest rate that, under any type of judicial criteria, is unacceptable.”

The battle between Argentina and its holdout creditors stems from 2001, when the country defaulted on billions of dollars in debt. Argentina offered to exchange the bonds it defaulted on for new bonds worth significantly less, a move that holdouts rejected. NML Capital sued Argentina seeking full repayment — principal and interest — and a Manhattan district court judge ruled that whenever Argentina paid one group of bondholders, it would also have to pay the holdouts.