The IRA did not threaten to return to violence, but its move on Wednesday underlined the political deadlock gripping the province since the group was accused by Britain and Ireland of mounting a massive bank raid in Belfast last December.
On Tuesday, the prime ministers of Britain and Ireland said the refusal of the IRA to disarm and end paramilitary activities was the only obstacle preventing the revival of a power sharing government set up under the 1998 Good Friday peace agreement.
"We reject this," said the IRA in a statement. "We do not intend to remain quiescent within this unacceptable and unstable situation. It has tried our patience to the limit."
The IRA, which has been observing a ceasefire in its campaign against British rule since 1997, had said it was willing to disarm as part of an overall deal.
But it rejected a demand from Protestant unionists - so called because they support Northern Ireland's political union with Britain - for photographs to be taken of its weapons being destroyed, saying this would be an unacceptable humiliation.
In December, a gang stole $49.87 million from the vaults of Northern Bank in Belfast and police said they believed the IRA was to blame.
The organisation has denied it was involved, and in the latest statement responded to the wave of criticism heaped upon it and its political arm Sinn Fein by saying it was taking the offer to disarm off the table.
"The IRA has demonstrated our commitment to the peace process again and again - we want it to succeed," said the statement. "But peace cannot be built on ultimatums, false and malicious accusations or bad faith."
But a spokesman of British Prime Minister Tony Blair insisted the IRA was involved in the bank heist.
"And therefore it is the IRA that is the sole obstacle in moving forward," said the statement from Blair's Downing Street office.