Martin said the new government will struggle to argue for a hard Brexit
The leader of Fianna Fáil has called the result of yesterday's General Election in the UK "very significant" for Ireland.
Martin said the new government will struggle to argue for a hard Brexit - where Britain would be taken out of the single market.
The Tories remain the biggest party with 317 seats so far and Labour currently have 261 - with 326 required for a majority and just two seats left to be called.
"They will not have the capacity to get it through parliament," he told Newstalk Breakfast. "Whatever is ultimately agreed must be able to pass that test.
"What that means in some respects is that we are looking at a very incoherent situation emerging, where you may not have a singular coherent voice within the Conservative party on how to proceed in relation to Brexit."
He added that Prime Minister Theresa May must also now consider her position as leader.
"Quite clearly she has lost seats and she has lost her majority. That in itself will have its own impact."
Labour leader Jeremy Corbyn reiterated his call for the Prime Minister to resign as he claimed it was "pretty clear who won this election".
Martin said European institutions need to respond appropriately to the election results.
"I think cool heads are required, and common sense must prevail," he said.