Enda Kenny was making a speech on the implications of Brexit on Wednesday.
He said the move posed a serious threat to the Republic's economic prosperity.
He also said the negotiations would be the most significant that Ireland had faced as an independent state.
Mr Kenny also warned that if no executive was formed after the election on 2 March, Northern Ireland would struggle to have its concerns heard.
While the UK as a whole voted to leave the EU, Northern Ireland voted to remain by a majority of 56% to 44%.
The border between Northern Ireland and the Republic of Ireland has been the subject of much discussion following the referendum, as it is set to become the UK's only land border with the EU.
"With the dissolution of the assembly, there is a very real danger that the absence of political leadership in Northern Ireland will lead to a retreat to partisan debate and an even greater marginalization of Northern Ireland's concerns," Mr Kenny said.
"The Brexit process will not wait for another round of lengthy talks in Stormont.
"When Article 50 is triggered, the world will move on, and it will move on quickly.
"Of course I will do my best to put forward the interests of the north in the Brexit negotiations."
Mr Kenny said he would defend the Good Friday Agreement, oppose a hard border, argue for free movement on this island of Ireland, seek EU funding for cross-border projects and protect the rights of EU citizens in Northern Ireland and the Republic of Ireland during negotiations.

The undefeated Manchester fighter, 26, was awarded a 117-110, 115-112, 117-110 verdict over his Liverpool opponent.
Flanagan was docked a point in the eighth round by referee Phil Edwards for using his forearm, after receiving repeated warnings for pushing.
But it made no difference at the Liverpool Echo Arena as 32-year-old Mathews slipped to a 10th defeat.
Flanagan has now won all 30 of his professional fights.
His promoter, Frank Warren, says "the obvious next fight" for him is against fellow Mancunian and holder of the WBA lightweight world title Anthony Crolla.
"We've made him a big offer," said Warren on Box Nation. "Let the two of them fight. There's no problem from our end. It's a fight that could be made.
"Other than that I like the Linares fight," he added, referring to Venezuelan three-weight champion Jorge Linares, who currently holds the WBC version of the world lightweight title.
Crolla is scheduled to defend his WBA lightweight title against Ismael Barroso at the Manchester Arena on 7 May.
It is a matter of vital national interest that there is no return to a hard border on the island of Ireland when the UK leaves the European Union, the taoiseach (Irish prime minister) has said.
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Terry Flanagan retained his WBO world lightweight title with a unanimous points decision over Derry Mathews.