Carinthia had announced Wednesday it was willing to buy back 11 billion euros ($12 billion) of bonds issued by the now defunct lender at 75 percent of their face value.
The bid, valid until March 11, needs to be accepted by at least two-thirds of the creditors of "bad bank" Heta Asset Resolution, the HGAA's wind-down unit.
But a group of bondholders -- who say they control more than 5 billion euros' worth of debt -- declared Thursday they would refuse any reduction in their claims.
The creditors include Germany's Commerzbank and a Dexia unit, according to Bloomberg.
"Any offer that doesn't foresee a full repayment of the claims is questioning the principle of legally defined, gilt-edged investments," the group said in a statement.
"In any case, Carinthia is clearly able to pay," the statement read, adding that the state's "assets" largely exceeded the amount offered.
A rejection could potentially bankrupt Carinthia, a small state of 500,000 inhabitants already saddled with 4.8 billion euros of debt.
Austrian Finance Minister Hans-Joerg Schelling had urged investors Wednesday to accept the "attractive offer" and avoid lengthy legal battles.
The saga is a legacy of late Austrian far-right political Joerg Haider, formerly premier of Carinthia who died in 2008.
Under Haider, HGAA expanded into the Balkans as well as Italy and Germany via acquisitions and risky investments, expanding its balance sheet fourfold to some 40 billion euros.
Bavaria's state lender BayernLB bought a majority stake in 2007 in HGAA but two years later, as the global financial crisis raged, the bank came close to collapse and Austria nationalised it.
After a bitter and long dispute, Austria finally agreed last November to pay Bavaria 1.23 billion euros to put an end to the feud.