A motion calling for compensation from Libya for IRA victims has been backed by all parties, except Sinn Fein.
The motion, tabled by DUP MLAs Jeffrey Donaldson and Nigel Dodds, was debated in the Assembly on Monday.
Sinn Fein President Gerry Adams said he supported the right to seek compensation, but said this motion was unfair and partisan.
Mr Donaldson denied that. He said it was an attempt to get behind victims, both Catholic and Protestant.
The motion called on the UK government to put pressure on Libya to award compensation.
It is understood the legal team engaged in the campaign for compensation from Libya for IRA victims have taken hundreds of enquiries.
More than 200 IRA victims are already involved in the case against Colonel Gaddaffi's regime which they believe supplied arms to the IRA in the 1980s.
The SDLP backed the motion but said they would have preferred a broader one recognising the violence perpetrated by agencies of the British Government and other paramilitary groups as well.
Mr Donaldson said he wanted the assembly to unite behind the campaign.
"It would significantly strengthen our case if we are able to tell the Libyan government that we enjoy full political support for our campaign," he said.
"This debate should not be viewed as a unionist-versus-nationalist issue as Libyan sponsored terrorism made no distinction between Protestant and Catholic or unionist and nationalist. This motion should be considered in the context of victims being heard and their quest for justice being aided."
Ulster Unionist Party leader Sir Reg Empey said that while he supports the pursuit of compensation from Libya, it must not be forgotten that "the triggers were pulled, the bombs planted, and the murder undertaken by people much closer to home".
Mr Donaldson and Mr Dodds plan to visit Libya to make the case for compensation directly to the Libyan government and have been working with victims from Northern Ireland, Warrington, London and Manchester.
During the Troubles, Libya supplied the IRA with tonnes of the explosive Semtex as well as thousands of rifles, small arms and flame throwers.
Last week, officials from Downing Street and the Foreign Office met with victims families to discuss the level of support they will receive to pursue their compensation claims.
However, the son of Libyan leader Colonel Gaddafi, Saif al-Islam Gaddafi, has said Libya will resist compensation demands.
He said any claims based on Libya's supply of explosives to the IRA would be a matter for the courts.
Prime Minister Gordon Brown had declined to put formal pressure on Libya for compensation, but he has said the UK will support families making claims.