The Democratic Unionist Party (DUP) has underlined its demand for the republican movement to confirm that the IRA is gone for good.
Sinn Fein dismissed the comment as ridiculous, coming a day after an Independent Monitoring Commission (IMC) report found the IRA had effectively ceased to exist.
The clash came ahead of talks between the DUP and Sinn Fein at Stormont aimed at securing the future of Northern Ireland's power-sharing government. The talks broke up with both parties committing themselves to further discussions.
The two parties are divided over a series of issues including the devolution of policing and justice powers, education reform, the future of the Maze prison site and the promotion of the Irish language.
The British and Irish Governments said the IMC report should clear the way for political progress, but the DUP wants assurances from republicans that the IRA will never return.
DUP deputy leader Nigel Dodds denied his party had an obsession with the IRA.
"The obsession on the issue of policing and justice is not on the part of unionists, it is on the part of Sinn Fein," he said.
"They are the people who continually raise this issue, although there is no great groundswell out in the community that that is the issue of primary importance."
Mr Dodds said the public was more concerned with bread and butter issues, but insisted community confidence in republican intentions had to be bolstered before justice powers were transferred to Stormont.
"For Gerry Adams to say 'well, you know the IRA are off the stage'... if that's the case, what's the problem then with saying that they're disbanded, they're gone for good?" asked Mr Dodds.
