Taoiseach Leo Varadkar has said that he will not be attempting to stop Government Ministers who want to travel to North Korea.
However, he added that they would not be allowed to travel as official representatives of the government.
Independent Alliance Ministers John Halligan, Finian McGrath and Shane Ross have asked to embark on a peace-building mission to North Korea.
Mr Varadkar said it is not his role to control what Ministers do in a personal capacity.
"I should say that there isn't going to be a Government mission to North Korea, and the Minister for Foreign Affairs has been very clear on that," he said.
"But I'm certainly not the keeper of any of my Ministers, so if they wish to travel to North Korea, I'm not going to be sending anyone to stop them at the airport but it certainly won't be a Government mission."