The new plan involves a Legacy Commission to investigate Troubles-related killings, a separate information recovery body, and a dedicated legacy unit within An Garda Síochána (Irish police).
A package of protections for veterans has also been proposed by the UK government.
But some MPs, including Northern Ireland MPs, have said the measures do not go far enough and want to amend the bill to include stronger protections in law.
Sir Chris told Irish broadcaster RTÉ that he worried that “some people have misunderstood the purpose of the bill”, adding that it was all about getting answers for families.
He said that would only happen if there is “transparency” from both Westminster and the Irish government.
On Tuesday, Sinn Féin MP John Finucane, whose father Pat Finucane was shot at his home in north Belfast by loyalist paramilitaries in 1989, said it “is clear that isn’t a problem of families misunderstanding the legislation, the concerns that they have are real, they are substantive”.
“The answer isn’t to explain the legislation better, it is to make the legislation better,” he added.
“Legacy is far too important to get wrong again and the objective isn’t simply to get legislation on to the statute books, the objective has to be to get it right for families who have already waited far too long for truth and justice.”
Finucane said that “essential to all of this has to be equality before the law, so nobody, absolutely nobody, including British state veterans should receive preferential treatment because of who they are, or who they served with”.
Democratic Unionist Party (DUP) assembly member Phillip Brett’s brother Gavin was murdered by loyalist paramilitaries in Glengormley, County Antrim, in July 2001.
He said it is “clear there are concerns right across the board with the proposals from the Labour government in relation to this legislation”.
“I think it is important to recognise that at the core of legislation we need something that deals with the need for victims and survivors because they have witnessed for years legacy here in Northern Ireland be corrupted, be that through the Belfast Agreement with the release of terrorists or be that through the royal prerogative of mercy given to people after the Belfast Agreement.”
“We are determined to deliver legislation that ensures that all people in Northern Ireland, all victims in Northern Ireland are able to get truth and justice,” he added.