Scottish independence is "a matter which is internal to the UK and Scotland", the Taoiseach has said.
Enda Kenny has argued it is "not appropriate for us to speculate about any possible scenarios around it" in the wake of Nicola Sturgeon's announcement of a second referendum.
Mr Kenny previously came under fire in Britain after he spoke up on behalf of Scotland at an EU Council meeting shortly after the Brexit vote.
Last June, the Taoiseach made the unprecedented intervention, telling other EU leaders that Scotland should not be "dragged out" of the EU against its will.
The move marked a dramatic shift in Government policy, as ministers had been warned to maintain a diplomatic silence during the 2014 independence referendum in Scotland.
However, his comments drew criticism from Theresa May's Conservative Party, which suggested he was "batting" for Scotland. Ukip accused him of acting as Ms Sturgeon's "gofer".
However, Mr Kenny has now softened his approach, indicating that he sees no impact on the question of Irish unity as a result of events in Scotland.
"The Good Friday Agreement sets out the basis on which unification could arise by peaceful and democratic means.
"Our primary objective is to ensure that all aspects of the Good Friday Agreement are fully protected under Brexit," he said.
Mr Kenny said the Agreement must be acknowledged in the Brexit deal because "that would mean that if at some point in the future the people of Northern Ireland wanted to join the Republic" they would be allowed back into the EU "seamlessly...in the same way East Germany joined West Germany after the fall of the Berlin Wall".