Dealing with legacy issues from the Troubles in Northern Ireland remains of "paramount importance" the Government has insisted, despite it not featuring in key legislation.
Northern Ireland spokesman Lord Dunlop said "intensive work" continued to build the broad consensus needed to bring forward proposals to deal with the emotive and divisive issue.
He moved to reassure peers as he presented The Northern Ireland (Stormont Agreement and Implementation Plan) Bill for its second reading.
The proposed legislation aims to implement parts of two political deals aimed at shoring up the country's fragile power-sharing administration as well as plans to establish a commission on paramilitary activity.
It also proposes making Assembly members commit to challenging paramilitary activity.
But in speaking to the Bill, Lord Dunlop told peers: "I would like briefly to address an issue that formed an important part of the fresh start talks, but which does not feature in this legislation.
"That is the establishment of new bodies to deal with the legacy of the past in Northern Ireland.
"I would like to reassure you it is of paramount importance to the Government, and it's clear it is important to peers as well.
"In discussions I have had in the run up to the debate many of you have raised this issue."
He added: "It is the victims and survivors who suffered more than anyone else as a result of the Troubles.
"The new institutions will therefore be balanced, proportionate, transparent, fair and equitable, allowing Northern Ireland to move forward and have the needs of victims and survivors at their heart.
"Intensive work therefore continues with victims' representatives and others on finding a way to build a broad consensus needed to legislate.
"I hope very much that legislation to establish the legacy institutions in a separate bill will be brought forward once the necessary consensus has been achieved."
Its absence from the Bill was also lamented by Labour former Northern Ireland Secretary Lord Murphy of Torfaen.
He said: "It is a disappointment that we haven't in this Bill references to the legacy issue in Northern Ireland.
"I don't think Northern Ireland can be settled until we deal with those issues.
"That issue has to be addressed.
"The issue of victims, survivors, of our communities in Northern Ireland - all that is dependent on how we deal with the past."
Liberal Democrat peer Baroness Harris of Richmond said it was "deeply disappointing" that no agreement had been reached over the "vexed issues of the past".
She said: "It's vital that a settlement is arrived at in which the victims of the years of violence and their families can have these issues resolved."
Former Ulster Unionist leader Lord Empey said the independent reporting commission was broadly welcome and would help to instil a degree of confidence.
Independent crossbencher Lord Eames welcomed the Bill but warned: "You cannot legislate for reconciliation in a divided society."
Paramilitarism was "still stalking our streets" and the legislation was by no means the end of the story.
Democratic Unionist Lord Browne of Belmont said the new independent reporting commission represented significant progress towards the "ultimate goal of eliminating paramilitarism".
But there were many problems still to be resolved, including "confronting the past".
Lib Dem spokesman Lord Alderdice said the political parties in Northern Ireland had "stared into the abyss" and decided to draw back.
He said the Bill represented something positive and the Government should be commended for bringing it forward.
The Bill was given an unopposed second reading and now goes forward to its detailed committee stage at a later date.