Lord Eames and Denis Bradley chaired the consultative group
The government has invited people to formally respond to the recommendations in the Eames Bradley report on Northern Ireland's past.
In January the group published their report on dealing with the legacy of conflict.
The consultation will run until October.
Its most controversial recommendation - making a payment to the family's of all victims - has already been rejected by the government.
The Secretary of State Shaun Woodward said "Dealing with the legacy of the events of the last 40 years remains one of the greatest challenges still facing Northern Ireland.
"The size of the challenge was underlined by the controversy which surrounded the report by the Consultative Group on the Past when it was published earlier this year.
"Their recommendation for a recognition payment was the subject of fierce and heated debate to the exclusion of the other recommendations. I have already made the Government's position on the recognition payments clear.
"But in a democracy we must allow all voices to be heard and it is essential that there is careful consideration given to the Eames/ Bradley proposals and I want to start that process today.
"Building a shared future which is not overshadowed by the past cannot be imposed by the Government on the people of Northern Ireland, it must come from the ground up.
"Therefore I would appeal to political leaders and the wider community in Northern Ireland to engage fully in a study of the proposals, look carefully at each of these recommendations to find the points of agreement on those issues which remain divisive.
"Whatever the outcome of this consultation, the Government will continue to work with the people of Northern Ireland on the path to reconciliation."