The Taoiseach's said there should be an independent public inquiry into the murder of Belfast solicitor Pat Finucane.
Leo Varadkar's comments came after the Finucane family lost a UK Supreme Court challenge over the decision not to hold a public inquiry into his murder.
But they won a declaration that an effective investigation into his death was not carried out.
The court unanimously found an investigation compliant with Article 2 of the European Convention on Human Rights was not done.
Mr Finucane represented IRA hunger strikers, and was killed in front of his family by Ulster Defence Association (UDA) gunmen at his home in February 1989.
The Finucane family had claimed that former British Prime Minister David Cameron reneged on a commitment, given to their family, for a public inquiry into the circumstances of his murder.
Speaking in London after the verdict today, his widow Geraldine Finucane said: "The judgement of this court is not the end of that journey, but it represents great progress towards the goal.
"The British government now knows that it cannot conceal the truth any longer".
While Mr Varadkar said: "The Government's position is that an independent public inquiry into the murder of Pat Finucane should be established, in line with the political commitments made by the British and Irish Governments at Weston Park in 2001.
"The Government has made this position consistently clear to the British government, and will continue to do so.
"I have met with the Finucane family in recent months, as has the Tánaiste, to confirm the Government's ongoing support for their search for truth and justice."
<blockquote class="twitter-tweet" data-lang="en"><p lang="en" dir="ltr">In the light of the judgment in the UK Supreme Court and the British Government’s political commitments made in 2001, a Public Inquiry into the murder of Pat Finucane must be established</p>— Leo Varadkar (@campaignforleo) <a href="https://twitter.com/campaignforleo/status/1100739129070026752?ref_src=twsrc%5Etfw">February 27, 2019</a></blockquote>
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