The parties outlined their opposition to the proposals in a virtual meeting with Mr Lewis, which also included Irish Foreign Minister Simon Coveney.
The meeting came as it was confirmed the Northern Ireland Assembly will be recalled next week from its summer recess to discuss concerns over what politicians and victims have described as a “de facto amnesty” for Troubles crimes.
Mr Lewis said on Wednesday that he intends to introduce legislation to create a proposed statute of limitations which would end all prosecutions for incidents up to April 1998 and would apply to military veterans as well as ex-paramilitaries.
It was a fairly robust conversation. Each of us outlined our views on the way forward in relation to legacy
Sir Jeffrey Donaldson
The proposals, which Prime Minister Boris Johnson said would allow Northern Ireland to “draw a line under the Troubles”, would also end all legacy inquests and civil actions related to the conflict.
Following the meeting on Friday, DUP leader Sir Jeffrey Donaldson said: “It was a fairly robust conversation. Each of us outlined our views on the way forward in relation to legacy.
“We recognise that these are very difficult and sensitive matters.
“This morning I have been meeting with some of the groups here representing innocent victims from across Northern Ireland. They are very concerned by the Government’s proposals for what they believe amounts to some form of amnesty.
“They believe passionately that the opportunity for victims and families to pursue justice should not be closed off and that view was replicated in the comments made by party leaders this morning.”
He added: “We want a process on legacy which includes an opportunity for those families and for those victims that want to take that route to pursue justice.
“It is not just about truth, it is not just about information recovery, it is about having the opportunity for individuals and families to pursue justice for their loved ones.”
Alliance Party leader Naomi Long said her party would not “provide cover for anything” that amounts to an “amnesty” over Troubles prosecutions.
Mrs Long said: “Alliance was clear with the governments that we will continue to engage in the legacy process in order to find a solution. But that solution needs to be based on the rule of law and due process.
“However, we will not provide cover for anything that amounts to an amnesty. I was clear in the meeting this process has to be centred on victims, who have been re-traumatised this week thanks to the actions of the UK Government
“Any suggestion their right to access justice has been denied will hurt them further.”
Ulster Unionist leader Doug Beattie said the meeting “did not provide any solutions for innocent victims”.
Mr Beattie said: “I made clear at the meeting that we would not be supporting a statute of limitations, which has always been our consistent position because it was always going to inevitably lead to an amnesty for terrorists.
“The UK Government must widen their proposals to incorporate a criminal justice element or they will risk inflicting more pain on innocent victims whose families have already sacrificed so much.
“Any proposals which snuff out any hope of justice need to be abandoned. The Irish Government needs to do more than what they are doing now. It`s not good enough that the Irish Government comes to the table with warm smiles, but little else. Where is their command paper and what are they going to do?”
Irish Taoiseach Micheal Martin said there has to be a “consensus-based approach”.
He said: “What is at the foremost of our minds at all times must be the victims and their families.
“They feel betrayed and they feel let down, and we have to prioritise the families and victims of so many atrocities during that period of our history on this island, irrespective of one’s community.
“It’s very clear people want those that murdered their loved ones, be it paramilitaries, should be fully accountable to the justice system, fully acknowledging the challenges around that.”
Stormont is to be recalled on Tuesday after more than 30 MLAs signed a recall petition introduced by the SDLP.
MLAs will debate a motion calling for victims and survivors to have a “full, material and central role and input into the content and design of structures to address the legacy of the past”.