The SDLP's Dominic Bradley called upon people with any information of the the whereabouts of the bodies of the disappeared victims of the troubles to contact the Independent Commission for the Location of Victims' Remains, on 16 April 2012.
Mr Bradley listed the names of seven of the disappeared whose bodies had yet to be recovered, and how the remains of others had been dug up in remote bogs.
"Information is the key to progress," he said.
The families of the victims, he added, were not asking for prosecutions "or even for the truth", they simply wanted the bodies to be returned.
The UUP leader, Mike Nesbitt, moved his party's amendment calling on the commission "to make clear what more can be done, and by whom, to bring the comfort of recovery to the remaining families".
He spoke of attending the funeral of Danny McElholm, a young man who was disappeared longer than he lived.
Mr Nesbitt said "seven stains remain upon the fabric of our society".
Sydney Anderson of the DUP said the remaining families were "still waiting and living a nightmare".
He described one of the disappeared, Jean McConville, as a young mother "whose only crime was to show compassion to a dying soldier".
Sinn Fein's Mitchel McLaughlin said they would support the motion as amended in order to avoid dividing the house on this matter.
He said the IRA came to "recognise the injustice" of their policy and ended it.
"It was an injustice then and it is an injustice now," he added.
In an intervention, Jim Allister of the TUV called on Mr McLaughlin to withdraw a statement he said the Sinn Fein MLA made in 2005 that the killing of Jean McConville "was not a criminal act".
Mr McLaughlin said he would address this in the context of a process of truth recovery.
Such a process would include the role of the British security services in procuring murder, he added.
Trevor Lunn of the Alliance party asked how those left behind could achieve closure without a body.
"It is unfinished business of the worst kind," he said.
When the debate continued after Question Time, the SDLP's Patsy McGlone spoke of meeting the mother of Columba McVeigh, one of those murdered by the IRA.
"That poor woman pined her way to her grave," he said.
Jim Allister of the Traditional Unionist Voice said those who sat on the Sinn Fein benches believed the "callous, cruel, vicious murder of Jean McConville was a justified and lawful act".
Alban Maginness of the SDLP also referred to Mitchel McLaughlin's 2005 comment about the death of Mrs McConville.
He said the killing was "a criminal act by anyone's standards".
The motion as amended was carried on an oral vote.
You can see the first part of the debate