Stephen Donnelly says he makes "no apologies" for mandatory hotel quarantine, despite pushback from the European Commission (EC).
The EC sent a list of questions to the government, raising concern about freedom of movement in the EU and the criteria used to determine the designated countries.
"I make no apologies to the commission or to anybody else for putting in place the measures that our public health teams believe are the right measures to keep people in this country safe," Mr Donnelly said.
"That's what we've done, and that's what we will continue to do."
Mr Donnelly says the system is doing exactly what we needed to do and "the commission is perfectly entitled to believe what it wants".
He added that the Government is still considering replicating the UK vaccine rollout which would see longer intervals between Covid-19 jabs in order to have more people innoculated against the virus.
"That is under active consideration by the public health officials right now," Mr Donnelly said.
"I think it's important to say, earlier today, I had by a mile, the most positive meeting I've had with with Dr [Ronan] Glynn in a Nphet briefing, the reality is, the plan is working.
"We are suppressing the virus here, we have very very positive results today hotel quarantining, and the other measures against important variance are working very well and critically, in spite of what has been a very rocky week for the vaccination programme."
Earlier, Dr Glynn had remarked that case numbers are "better than could have been hoped for" just a few weeks ago.
Mr Donnelly said he was sure the government currently have "ready to go" several times more vaccinators than we need to handle the vaccine roll-out.