The NI Office (NIO) has published guidance on how an independent board overseeing a new victims payments scheme will assess eligibility.
It will assess people with convictions of more than two and a half years to determine if a payment is appropriate.
The scheme was legislated for in January.
Factors may include an individual's age at the time of conviction or whether they have shown remorse.
Where someone has tried to cause serious harm to another, a payment is likely to be not considered appropriate.
In certain special circumstances the board may decide someone without a conviction of more than 30 months is ineligible - for example when an individual has been found by a civil court to be liable for a terrorism-related incident.
Government sources have expressed frustration at the continuing failure of the NI Executive to designate a department to administer the victims payment scheme.
Disagreements "a distraction"
The sources say Stormont ministers are under a legal obligation to implement the pensions.
The sources say they do not accept that disagreements over whether London or Stormont should fund the scheme are a valid reason for delay, describing them as a distraction from the immediate task of designating a department to take responsibility.
NI Secretary Brandon Lewis said on Friday the "moral and legal obligation to deliver this scheme for victims of the Troubles injured through no fault of their own is undeniable" and he hoped that the publication of the guidance will "renew the focus and efforts of the Northern Ireland Executive to move forward to finally deliver for these victims".
"The political disagreements and delay of the last few years on this issue have gone on long enough," he said.
"It is imperative that Sinn Féin now enable the scheme to move forward by agreeing with all the other parties and urgently designate a department to administer the scheme and get payments to those who will benefit most."
He added: "I think it's absolutely dreadful the people who have waited far too long, are still being kept waiting, not only do they have that moral right to this and I think we all agree on, they have a legal right now."
In a statement on Friday, the Commission for Victims and Survivors said it had been briefed on the new guidelines but added: "We are taking legal advice on the impact of this decision and will consider that advice before making further comment."
NI Deputy First Minister and Sinn Féin vice-president Michelle O'Neill has tweeted that on Thursday she had discussed "legacy and victims issues with British PM" and on Friday she had a "call with Brandon Lewis".
"It's crystal clear that they are not listening to concerns," she added in the tweet.
"The British government are intent on the politics of exclusion and playing politics with the needs of victims."
NI First Minister and DUP leader Arlene Foster said she welcomed the guidance.
"This is another small step along the road to innocent victims receiving a pension which they rightly deserve," she said.
"It is right and proper that victim makers are not able to avail of this pension.
"It would be wholly wrong for bombers to be awarded a pension."
Mrs Foster called on Sinn Féin "to make the needs of innocent victims, from all over the British Isles and of all political backgrounds, a priority and allow the pension to move forward".