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.
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.