Secretary of State James Brokenshire has pledged to publish plans to deal with the legacy of the Troubles - even if a deal isn't reached at Stormont.
Mr Brokenshire said while he would prefer that progress on the draft proposals was accompanied by an agreement to restore the Executive, he was obliged to act in the best interests of victims.
A group of victims held face-to-face talks with the Secretary of State in Co Antrim yesterday.
They asked him to immediately begin the long-awaited public consultation on draft legislation.
Three years ago, the Stormont House Agreement set out a plan for dealing with the past, including the setting up of an Historical Investigations Unit to examine unsolved murders.
A truth recovery body and an oral history archive were among the initiatives agreed by politicians in 2014, but political wrangling has halted further progress.
The following year, the Fresh Start Agreement failed to break the deadlock on issues such as the Government's national security veto on sensitive files.
London is to provide £150m to fund the new bodies.
After the meeting in Templepatrick, Mr Brokenshire said he had heard the victims' message "loud and clear".
He said: "Clearly I feel under an obligation to move forward to see that victims and survivors are able to get that sense of progress that they have been asking for, for such a long time.
"It is a very long time since Stormont House itself was concluded. It has taken too long, we can't wait much longer and I am intent to see that we do make progress.
"The focus is very firmly on seeing the re-establishment of an Executive, but if that proves intractable, if that does not prove possible, then obviously I think the victims have waited for a very long time and we do need to move this forward."
The Secretary of State said a consultation was a way of building momentum towards implementing the Stormont House proposals.
Victims' Commissioner Judith Thompson and members of the Victims and Survivors Forum - a body representing people affected by the Troubles - said the public consultation must begin as soon as possible.
While victims welcomed parts of what Mr Brokenshire said, some were disappointed that he didn't give a firm date for starting the consultation.
Robert McClenaghan's grandfather Philip Garry was killed in the McGurk's Bar bombing carried out by the UVF, which the authorities initially blamed on the IRA.
"My father has now reached the ripe old age of 87, so it's important for us that we try to get some acknowledgement and some truth before he passes on," he said.
Hazel Deeney's husband Trevor was murdered by the INLA in 1998 and buried on the day the Good Friday Agreement was signed.
She said Mr Brokenshire was compassionate and understanding, but was hampered by the lack of a Stormont Executive.
"I do believe he could have went further and I do think the Executive getting up and running plays a crucial part in how victims' (needs) moving forward are going to be met," she said.
Ms Thompson said victims were weary, frustrated and disillusioned at the lack of progress on the Stormont House mechanisms.
She added: "It undermines people's trust and respect for the way that governments and the law are dealing with them."
She stressed the need for a "victim-centred approach" that was balanced, fair and inclusive.
She said: "It is almost two years to the month since the Fresh Start Agreement abandoned victims and survivors, and it is with real sadness that we find ourselves once again in a political stalemate.
"In advocating for a legislative consultation, the commission and the forum are very conscious that there will be challenges."