Leo Varadkar says Ireland's objectives have remained the same for two years
The Taoiseach says the Government has noted the departure of Boris Johnson and David Davis from the British cabinet, but is still hopeful that an agreement on Brexit can be reached.
Leo Varadkar said he waited with anticipation for the upcoming 'White Paper' from Prime Minister Theresa May.
The document will detail the British government's Brexit proposals.
It is still set to be published this week as planned, despite Mr Davis and Mr Johnson resigning only days after Mrs May's cabinet reached an agreement on their Brexit position - including for a proposed UK-EU free trade.
On Tuesday, two more British Conservative politicians stepped down from their positions, with Ben Bradley and Maria Caulfield leaving their roles as vice-chairs of the party.
Speaking in the Dáil amid the political turmoil across the Irish Sea, the Taoiseach said the Irish Government's position on Brexit has not changed.
He stated: "I firmly hope that what we saw from [Mrs May's country residence] Chequers on Friday, what we will see in the White Paper later this week... at long lost represents an agreed UK government position on what they want the future relationship to look like.
"We have always known what we want it to look like - first, to protect the Common Travel Area; second, to continue to have free trade between Britain and Ireland; and, third, to avoid a hard border on our island."
He added: "They are our objectives - they have been our objectives for two years. They are objectives which I think we can achieve."
Mr Johnson and Mr Davis have been replaced as foreign and Brexit secretaries by Jeremy Hunt and Dominic Raab respectively.
The EU's chief Brexit negotiator Michel Barnier, meanwhile, does not believe a new man in the job opposite him will make much difference.
He observed: "As the EU negotiator, I will negotiate only with the British government - with the negotiator appointed by Mrs Theresa May.
"Our next round of negotiations will be next Monday, with the British delegation appointed by Mrs May."