The Tánaiste says the Government does not want to veto the progression of Brexit talks, but that more progress on the border issue is needed.
Foreign Affairs Minister Simon Coveney says they do not want to delay negotiations moving on to phase two.
However, he stressed that Britain needs to offer solutions on avoiding a hard border.
His comments to the BBC's Andrew Marr come ahead of a crucial meeting tomorrow between British Prime Minister Theresa May and European Commission President Jean Claude-Juncker.
That meeting is seen as an important deadline for the UK, ahead of a key summit of EU leaders on December 14th.
At the summit, the officials will formally decide whether enough progress has been made to progress talks to examining the future relationship between the UK and EU.
The President of the European Council Donald Tusk has said that EU will not accept any proposal on the border without Ireland’s agreement.
Minister Coveney explained: "The Irish government, just like the British government, wants to be able to move the Brexit process on to phase two.
"There is no desire, I can tell you, in Ireland to delay this process. At the same time, we have a responsibility as a government to represent the interests on the island of Ireland, north and south.
"We believe that Ireland, as an island, is uniquely vulnerable and exposed to a potential bad outcome from Brexit. That is why we are looking for more progress than we have."
— BBC News (UK) (@BBCNews) December 3, 2017
On the same BBC programme, Conservative politician Jacob Rees-Mogg appeared to attempt to link the Irish Government's position on Brexit to the recent internal political crisis involving Frances Fitzgerald - despite Minister Coveney now having taken over as Tánaiste.
Mr Rees-Mogg - a 'Tory traditionalist' and prominent opponent of the EU - claimed: "Irish politics are quite complicated at the moment... there's a vote of no confidence in the deputy prime minister, they are worried about an election.
"I think the Irish border has become a matter of immediate political concern in the run-up to a potential general election and the strength of Sinn Féin."
A number of British publications have made similar claims in recent weeks.
Simon Coveney last month dismissed as 'nonsense' an article in The Sun which claimed that the Government is only now starting to fight against a hard border.