The Taoiseach has written to British Prime Minister Boris Johnson urging him to implement a full inquiry into the murder of Belfast solicitor Pat Finucane.
Micheál Martin met with the Finucane family on Monday and wrote to the Prime Minister shortly after.
It's understood that the two leaders are scheduled to have a phone call on the matter on Friday, once an appropriate time can be agreed.
Mr Finucane's family has thanked the Irish Government for their unanimous support for their campaign.
The Taoiseach, who dealt with this issue when he was Minister for Foreign Affairs, spoke with Pat's son, John Finucane and widow Geraldine on Monday, and offered his full support.
"He made it very clear we had the full support of the Taoiseach's office and he committed to engage with Prime Minister Boris Johnson," John Finucane said.
In October, Northern Ireland Secretary of State, Brandon Lewis pledged to make a decision on November 30 on whether or not to order an inquiry.
A Seanad resolution on the issue was supported by all parties and independents. Likewise, Thursday's Good Friday Agreement Committee was unanimous that the British Government must push forward with the inquiry.
Pat Finucane was aged 39 when he was shot dead in front of his children by UDA loyalist paramilitaries in his north Belfast home while eating dinner.
In 2012 a government-commissioned review found agents of the state were involved in the killing.
John Finucane, now the MP for North Belfast, said: "We were very grateful that Minister Simon Coveney attended and spoke so forcefully at that hearing last night, and again this morning at the Good Friday Agreement committee.
"When they agreed to have an inquiry if a judge recommended that inquiry, but here we are, 31-years after his killing, nine years after the then Prime Minister David Cameron sat in front of me and accepted that there was collusion on behalf of the British state and the people who came into our house in February 1989, we are still campaigning for the inquiry that has been promised."
"It is over to the British government. I don't think they're in any doubt as to what the world thinks and pressure has also been brought to bear from the committee of ministers.
"There's very little room for the British government to move to, they have a judgement from the highest court within their own jurisdiction that they must answer."
Twenty-four members of US Congress have also released a letter to the British Prime Minister calling for an independent public inquiry into the murder, stating that they are “astounded” that British Government has not yet done so.
Mr Finucane says they have received contact in recent days from the British government to organise a meeting.
"Within the past couple of days we just had confirmation that there will be a virtual meeting on Monday at noon, with the Secretary of State, but apart from that agreement we don't have any expectation or idea what it is that they will present to us to fulfil their legal, domestic and international legal and human rights obligations," he said.
Mr Finucane said the campaign has taken its toll on his family.
"My mum was 39 when my father was killed, they had the best years of their life ahead. She was left with his three children, not just without a husband, but also, a very cruel and delivered context where she was seen as no better than a widow of somebody who deserved what he got," he said.
"The word collusion was very much a dirty word. If you uttered that word you were viewed through a certain lens as nothing more than a Republican propagandist.
"I think the campaign that we have had wouldn't have been possible without her strength, I can only imagine what she went through, and it does take a toll on all of us."