(Adds details, quotes from mediator Pollack, background)
By Hugh Bronstein
BUENOS AIRES, Feb 19 (Reuters) - The mediator in the case brought by investors who rejected Argentina's 2005 and 2010 debt restructurings said on Thursday that the "holdout" investors offered to reopen talks with Buenos Aires, but the government had not responded.
The case is part of years long, cross-border litigation following Argentina's sovereign debt default in 2002, after which some debt holders agreed to accept reduced payouts while others refused and took to the courts.
New York-based mediator Daniel Pollack said in a statement that the hedge funds involved in earlier talks passed the invitation through him to Argentina's lawyers in January.
Argentina "neither accepted nor otherwise responded to the invitation by the bondholders," Pollack said. The economy ministry could not be immediately reached for comment.
"The invitation by the bondholders was without pre-conditions and offered the possibility to the government of Argentina of a settlement without any present payment of cash, details to be negotiated," the statement said.
Pollack said the judge handling the case asked him to issue the statement.
Buenos Aires said last year that the Rights Upon Future Offerings (RUFO) clause in the restructured debt contracts blocked it from settling with the hedge funds on better terms than investors got in the 2005 and 2010 exchanges.
The clause expired at the end of 2014. Even so, Argentina signaled earlier this month that it would maintain a tough stance with bondholders the government denigrates as "vultures".
"What they're demanding can't be paid. You can't mortgage the country like that," Economy Minister Axel Kicillof told Radio del Plata on Feb. 10.
A U.S. court halted payments on the restructured bonds until a deal was reached between the holdout creditors and Argentina. But Buenos Aires defied U.S. District Judge Thomas Griesa's order and in late June moved to make a scheduled coupon payment by transferring money to BNY Mellon.
Griesa ruled the payment illegal and ordered it returned. Argentina refused, leaving BNY Mellon stuck in the middle and investors without their coupon payment.
Paul Singer, the founder of hedge fund Elliott Management, and one of the lead holdout creditors, told his investors in a letter dated Jan. 30 that the firm remains vigilant in its pursuit of a potentially huge windfall investment in unrestructured Argentine sovereign bonds. (Additional reporting by Nicolas Misculin; Editing by Grant McCool)