The Taoiseach has repeated a request for the British government to hold a public inquiry into the murder of Belfast solicitor Pat Finucane.
Micheál Martin and British Prime Minister Boris Johnson held a 40-minute phone call last night, during which the death of Mr Finucane in 1989 was raised.
Mr Finucane was shot dead by loyalist paramilitaries in front of his family amid claims of collusion between the killers and security forces.
Earlier this week Minister for Foreign Affairs Simon Coveney told the Seanad of the urgent need for a full public inquiry which, he said, would be "...a powerful demonstration of the UK government's commitment to peace, justice and reconciliation".
Four Stormont parties - Sinn Féin, the SDLP, Alliance and the Greens - have backed the Finucane family's demand for a public inquiry.
John Finucane, the Sinn Féin MP for North Belfast and son of Pat Finucane, has welcomed the Irish support for a public inquiry into the killing.
The Northern Ireland Secretary, Brandon Lewis, is due to make public the British government's position on an inquiry on Monday.
Any announcement of an inquiry would represent a major shift by the British government, with successive Conservative and Labour administrations resisting any such commitment.
Mr Martin and Mr Johnson also discussed Brexit negotiations, with the British Prime Minister underlining his commitment to securing a Brexit deal that "respects the sovereignty" of the UK.
A spokesperson for the Taoiseach said while nothing is guaranteed both Mr Martin and Boris Johnson want a deal agreed.
They spoke about the short time left to reach an agreement and the urgent need to resolve the outstanding issues.
A Downing Street spokeswoman said the men discussed the progress in the UK-EU negotiations.
"The leaders also reaffirmed the need to prioritise the Good Friday Agreement and avoid a hard border on the island of Ireland."
The Downing Street statement said: "The leaders updated one another on their respective efforts to tackle coronavirus and the steps they have taken to ensure people in the UK and Ireland can enjoy Christmas as safely as possible.
"They also discussed shared challenges including the environment and committed to working together ahead of the UK-hosted COP26 summit next year."
The statement concluded that Mr Martin and Mr Johnson "look forward to seeing one another in person when possible".
The European Union's chief negotiator Michel Barnier and his UK counterpart David Frost are resuming in-person Brexit talks in London today.
Time is tight to secure a free trade deal between the two sides, with the transition period set to end in just over a month.
But Mr Barnier, arriving in London yesterday evening, told reporters that he would continue to work with "patience and determination" to reach an agreement.
Face-to-face negotiations were paused last week after one of the EU team tested positive for coronavirus.
Mr Barnier tweeted earlier yesterday that the "same significant divergences persist" between the UK and EU.
Talks have been deadlocked for months over the issues of fishing rights, the governance of any deal, and the "level playing field" conditions aimed at preventing unfair competition by cutting standards or increasing state subsidies.