Taoiseach Leo Varadkar has said a US-Canada border would not be an acceptable option for the island of Ireland post-Brexit.
Theresa May has indicated she is looking at the customs arrangements between the US and Canada as a way of solving the Irish border issue created by Brexit.
Mr Varadkar said he had not heard Mrs May's speech at Westminster so he did not want to comment directly, but he did discuss his visit to the US-Canada border.
"I visited the US-Canada border, I visited it back in August, and I saw a hard border with physical infrastructure with customs posts, people in uniforms with arms and dogs and that is definitely not a solution that is one that we can possibly entertain," Mr Varadkar said.
The Taoiseach made the comments after a meeting with Luxembourg Prime Minister Xavier Bettel at Government Buildings in Dublin.
Mr Bettel said after the terrorist attacks in Paris in November 2015 Luxembourg had border controls and they had impacted the economy.
"For the moment I can't tell you about Theresa May's plans," Mr Bettel said.
"I want to see them, I want to read them, and then I'll be able to tell you if these are acceptable or not."
Asked if he was frustrated by the UK Government, Mr Varadkar said: "No, no, I never get frustrated by the British and I'm always very patient."
Mr Bettel said solutions were needed because the time is ticking.
"We started with a hard Brexit, now some people spoke about a soft Brexit, I want an intelligent Brexit," the Luxembourg PM said.
"We should be able to find the best way where we don't punish but it's not time for cherry-picking and we need a level playing field."
Prominent British Brexiteer Jacob Rees-Mogg has accused Ireland and the EU of risking a "no deal" Brexit with their "absurd" suggestion that Northern Ireland should be in a common regulatory area with Brussels to avoid a hard border.