US District Judge Thomas Griesa has criticised Argentina's decision to default on $29 billion in debt this week rather than pay holdout investors as ordered.

Judge Griesa told lawyers for Cleary Gottlieb, which represents Argentina, to stop what he referred to as 'misleading' information being released by the country regarding its battle with investors.

Some elected officials in Argentina have repeatedly stated that they had met their debt obligations, which the judge described as a "halftruth."

"The republic has issued public statements that have been highly misleading, and that has to be stopped," he said.

Judge Griesa had ordered the nation to pay $1.33 billion plus interest to NML Capital, a unit of Elliott Management Corp, and Aurelius Capital Management, the two leading US hedge funds who were not among those who agreed to accept new bonds after the nation defaulted in 2002.

Argentina argues that by depositing $539 million for a scheduled coupon payment in the account of its trustee, Bank of New York Mellon, that it had satisfied its obligation to pay its debts.

Mr Griesa had ordered BNY Mellon not to transfer that money to bondholders that exchanged debt in 2005 and 2010.

The hearing was called to map a course outlining where to go next.

"What occurred this week did not extinguish or reduce the obligations of the Republic of Argentina," the judge said.