Four Stormont parties have called on the British government to reconsider the decision not to hold a public inquiry into the murder of Pat Finucane.
The ruling out of an immediate inquiry has been branded an insult by the family of the late Belfast solicitor, who was gunned down by loyalist paramilitaries colluding with the British state in 1989.
On Monday, Northern Ireland Secretary Brandon Lewis said he was not taking a public inquiry off the table but said further examinations of the case by police and a police watchdog should conclude first.
Mr Finucane, 39, who represented republican and loyalist paramilitaries during the conflict, was shot dead in his family home in north Belfast in February 1989 by the Ulster Defence Association (UDA) in an attack found to have involved collusion with the British state.
The four parties wrote to Mr Lewis as Mr Finucane's son John signalled an intent to enlist the support of US President-elect Joe Biden.
Mr Martin also indicated that he would raise the issue with Mr Biden.
The letter signed by Sinn Féin's Michelle O'Neill, the SDLP's Colum Eastwood, Alliance deputy leader Stephen Farry and the Green Party's Clare Bailey urged a rethink.
They said the British government's decision was "neither a credible nor tenable position".
"It was an insult to the Finucane family," the senior party figures added.
"Your approach to this matter is now a matter of serious public concern.
"To avoid a public inquiry, you have clearly made a calculated decision to embark on a high-risk distraction strategy that now places both the Office of the Police Ombudsman and the PSNI in the midst of a historic murder investigation at a time when the intent is to take legacy out of policing.
"Your suggested approach potentially risks wider confidence in the rule of law and the administration of justice."
The issue has divided political opinion in Northern Ireland and several unionist politicians have welcomed the British government's decision, arguing that a public inquiry is not justifiable when so many other bereaved families remain waiting for answers.
On Tuesday, DUP MLA Paul Givan told the Stormont Assembly that the pain felt by the Finucane family was also felt by many other families.
"Of course the murder of Pat Finucane was wrong," he said.
"I acknowledge the barbaric nature of it as he was murdered in front of his family. One can only imagine the trauma that that has caused and it is clearly evident to this day - 31 years later.
"That pain is felt by thousands of people right across Northern Ireland. I think of La Mon. I think of Bloody Friday. I think of Enniskillen and Narrow Water (all IRA atrocities). The list goes on of thousands of people who suffer as a result of the terrorist campaign of over 30 years in this country.
"Many of those families have had but a mere desktop exercise carried out by the Historical Enquiries Team (HET)."
Mr Givan said there had been multiple investigations into the circumstances of Mr Finucane's murder.
"Thousands of victims of terrorism could only wish for the same level of interrogation to have taken place into the murder of their loved ones," he said.
"Victims have heard loudly the special status being afforded to the Finucane family by a range of political parties in this House and, indeed, by other international political figures."