The British Government has been accused of delaying a deal on addressing the legacy of the conflict as Northern Ireland negotiations reach a critical stage.
Northern Ireland Secretary James Brokenshire is blocking access to justice for families who have waited 45 years, Sinn Fein claimed.
Mr Brokenshire said they had a duty to victims to deal with past violence which left 3,637 dead and countless more injured.
Irish Foreign Affairs Minister Charlie Flanagan said there was a chance over the next few days to resolve legacy issues "once and for all" as the deadline to restore political power-sharing looms on Monday.
Sinn Fein negotiator Conor Murphy said: "The British Government has been kicking this can down the road forever and the reality is it is not a matter of what the political parties need.
"There are families out there waiting 45 years for access to justice.
"The British Government cannot continue to deny them access to justice."
The Democratic Unionists and Sinn Fein have been at loggerheads over funding for inquests into deaths during the 25-year Troubles.
Power-sharing collapsed in January after a row over a botched green energy scheme predicted to cost the taxpayer up to half a billion pounds.
Sinn Fein has said it will not share power with the Democratic Unionists' leader Arlene Foster as First Minister until a public inquiry into the Renewable Heat Incentive (RHI) is concluded.
The parties only have until 4pm on Monday to resolve their differences or face another snap election.
Mr Murphy added: "It is a critical time here. The clock is ticking."
The Ulster Unionists have warned there is limited potential for a deal to be struck in time.
Chief negotiator Tom Elliott said: "Whether we can make the deadline is still questionable.
"We have no idea how long the talks will go on for or if they will go beyond that 4pm Monday deadline.
Mr Brokenshire said discussions had been constructive.
"There are a number of issues where I see common ground and where I firmly believe that resolution can be achieved."
Mr Flanagan said it was important agreement was reached on Monday.
"Often minds are focused intensively once clocks are ticking loudly and once deadlines are looming.
"We are now entering that phase."