Taoiseach Micheal Martin has contacted Boris Johnson, calling for the UK Government to hold a full public inquiry into the murder of civil rights layer Pat Finucane.
North Belfast MP John Finucane told an Irish parliamentary committee on Thursday that the Irish premier had engaged with the UK prime minister on the matter.
The Sinn Féin MP and his mother, Geraldine Finucane, met Mr Martin earlier this week for the first time.
"He didn't need us to explain to him the significance and importance and the need for an inquiry into the murder of my father, and he committed to and I understand has already engaged with Boris Johnson on this issue," Mr Finucane told the committee. Pat Finucane, 39, was shot by loyalist paramilitaries in front of his family in 1989 amid claims of collusion with state security forces.
Mr Finucane told the committee that in February 1989 his family had "sat like many other families" enjoying their Sunday dinner around the kitchen table when "two gunmen burst in and shot my father 14 times and shot my mother once in front of us all".
The Sinn Fein MP said one of the most significant moments in the family's campaign to seek justice was when British prime minster David Cameron apologised for the British state's collusion in the killing.
"In October 2011 I sat in 10 Downing Street along with my mother and the rest of my family as we listened to the then-prime minister David Cameron explain to us and apologise for collusion that took place between the British state and killers that came into our house and killed my father," he said
"That for me was one of the most significant points in our 31-year campaign."
Mr Finucane said: "There is only one option left for the British Government to do and that is to have an inquiry, to have the inquiry that they promised, the promise they made to my family but also to the Irish Government.
"The inquiry in which they have resisted, and put all of their time and their efforts and all of their considerable resources into resisting for over 30 years."
He said a fully independent public judicial inquiry was the "only mechanism" that could "fully grasp all of the issues" that led to his father's murder.
"The British Government needs to heed and read the room with where this issue is going. It's not going away," he said.
In February last year, the Supreme Court ruled that investigations into the fatal shooting of the solicitor have not been effective and fell short of international human rights standards.
Northern Ireland Secretary Brandon Lewis has indicated that a decision over how the Government will proceed will be announced.
John Finucane said: "The Irish Government's position, his position (the Taoiseach's) is very clear, that there needs to be a strong response to the Supreme Court victory of last year.
"That response needs to be a public inquiry. "
On Sunday, it emerged that four of Northern Ireland's political parties have united to call for a public inquiry into the murder of Mr Finucane.
Four of Northern Ireland's six largest parties wrote a joint letter to Mr Lewis urging a public inquiry.
The letter - signed by senior members of Sinn Féin, the SDLP, Alliance and Green Party - emphasises that establishing the full facts around the killing is a matter of "the utmost public interest" and that "only a public inquiry can now assist the Finucane family to get the truth about the scope and extent of state collusion into Pat's killing".
The letter went onto say that holding a public inquiry would provide the British government with an opportunity to restore wider confidence in the rule of law and the administration of justice.
The letter is signed by Sinn Féin vice president Michelle O'Neill, SDLP leader Colum Eastwood, Alliance deputy leader Stephen Farry and Green Party leader Clare Bailey.
Sinn Féin MP John Finucane recently wrote to every member of parliament asking for their support for the family's cause.
In his letter, he contended "only a public inquiry can assist in ascertaining the true extent and scope of British state collusion in the killing of my father", adding that it was a matter of public interest not just in Ireland, but internationally too.