(Adds analysis on impact of possible contempt order)
By Joseph Ax and Andrew Chung
NEW YORK/BUENOS AIRES Aug 8 (Reuters) - The U.S. judge in Argentina's long-running debt battle with hedge funds threatened a contempt-of-court order on Friday if the nation did not stop issuing false statements about having made a required debt payment on restructured sovereign bonds.
U.S. District Judge Thomas Griesa in Manhattan railed at Argentina's lawyers from Cleary Gottlieb Steen & Hamilton following the publication of another so-called legal notice insisting the government has met its payment requirements and was therefore not in default.
Griesa said these notices were "regularly" and "systematically" omitting the vital obligations of the Republic.
Holding a newspaper copy of the notice, which appeared Thursday, Griesa said if the false statements did not stop, a contempt of court order will become necessary.
Griesa said he was not going to go further than a warning for now, but that could change. He repeated that the two sides must continue negotiating with the aide of mediator Daniel Pollack.
"We will continue to work tirelessly to defend the rights of Argentina," Economy Minister Axel Kicillof said on public television in Argentina, adding that at the hearing in New York on Friday, "Judge Griesa did not resolve anything.
"He created this confusing and extraordinary situation," said Kicillof, who also played down concerns the case would cripple investment in Argentina.
Griesa did not specify whether he would seek to sanction Argentina or its lawyers, though he said he was "glad" to hear Jonathan Blackman, Argentina's lead lawyer, say his firm, Cleary Gottlieb, did not aid in preparing the government's latest legal notices.
In rare circumstances, U.S. judges have held foreign governments in contempt and imposed monetary penalties. But such sanctions can be difficult to enforce, and federal appeals courts have split on whether foreign governments can be held in contempt at all.
Federal law largely protects the assets of foreign governments held in the United States, said Michael Ramsey, a professor of international law at the University of San Diego.
"You can't put Argentina in jail, so I'm not sure what he'd have in mind besides monetary sanctions," Ramsey said. "Argentina has refused to pay a valid judgment and I don't see why it wouldn't also refuse to pay a valid contempt order."
Blackman also complained of being attacked and lampooned by the lobby group American Task Force Argentina, which is partly funded by holdout investors.
Argentina missed a coupon payment after a grace period ended on July 30, pushing it into default on restructured debt from a previous default in 2002 on roughly $100 billion in sovereign bonds.
The government settled with nearly 93 percent of its bondholders in two restructurings but two deep-pocketed distressed debt investors held out and did not participate in the exchanges in 2005 and 2010. They are by far not the only holdouts, but have been the most prominent in their fight for full repayment on debt they bought at pennies on the dollar in a case that essentially comes down to a contract dispute.
Griesa, in 2012, awarded these holdout investors led by NML Capital Ltd, an affiliate of the $24.8 billion hedge fund Elliott Management Corp, and Aurelius Capital Management, who won a $1.33 billion judgement.
Argentina insists it is not in default because it deposited a $539 million coupon payment on exchanged bonds before a June 30 deadline. Griesa has called the deposit with trustee Bank of New York Mellon illegal and reiterated on Friday that, "there has been no payment."
Payments to exchange bondholders have not been made because of Greisa's order, which stipulated the nation must concurrently pay the holdouts their award plus accrued interest.
NOTICES AND CONTEMPT
Argentina has published legal notices in recent weeks disparaging Griesa and Pollack, who succeeded in getting the two sides to meet face-to-face for the first time in nearly 13 years but could not get them to an agreement by a July 30 deadline.
Pollack issued a statement after the hearing saying it was his intention to "convene and conduct further negotiations until a solution is reached, however long that may take."
The government accused the veteran judge of overstepping his purview and interfering in the affairs of a sovereign nation.
Argentina insists it cannot meet the demands of the court order, nor make a deal with the holdouts that is better than the terms offered in its two restructurings based upon a clause in its agreement known as the Rights Upon Future Offers (RUFO).
The RUFO clause expires on Dec. 31, 2014.
Reuters IFR has reported that private banks are trying to reach an agreement with the holdouts that would pay them 80 cents on the dollar for their Argentine bonds in hopes of getting the frozen coupon payment sitting at BNY Mellon released as soon as possible. (Additional reporting by Andrew Longstreth and IFR's Joan Magee and Davide Scigliuzzo in New York, Richard Lough and Hugh Bronstein in Buenos Aires. Writing by Daniel Bases; Editing by W Simon, Andrew Hay and Andre Grenon)