The defense comes as senior Republicans criticised the executive order
White House staff have been defending President Donald Trump's travel ban.
His executive order has created chaos over the weekend and has led to demonstrations at a number of US airports.
The refusal to grant entry to refugees and citizens from seven Muslim-majority countries has been widely condemned by world leaders.
Foreign Affairs Minister Charlie Flanagan says although US immigration policies are a matter for the US authorities, the ban could have far-reaching implications.
President Trump's adviser Kellyanne Conway told Fox News Sunday: "You're talking about a hundred and some who have been detained who are prevented from gaining access to aircraft in their home countries.
"They must stay for now, that's 1%, and I think in terms of the upside being greater protection of our borders and people, it's a small price to pay."
White House chief of staff Reince Priebus also said they would "apologise for nothing", but added to the confusion over whether people who have green cards, which would normally give them the right to come to the US without a visa, would be allowed to enter.
In an interview with CBS News he said they would be allowed to enter, but then added that they would be subject to extra checks.
He also said it might be possible that the number of countries included in the ban would be increased, possibly to include Pakistan.
Senior Republicans have criticised the executive order banning people from seven Muslim countries from coming to the US.
Senator John McCain said the President's order has been "confusing" and raised a number of questions.
He said the order, which has led to hundreds of people being detained at airports around the world and unable to fly, could give Islamic State propaganda material.
Sen McCain and his fellow Republican Senator Lindsey Graham said in a joint statement: "We fear this executive order will become a self-inflicted wound in the fight against terrorism.
"This executive order sends a signal, intended or not, that America does not want Muslims coming into our country. That is why we fear this executive order may do more to help terrorist recruitment than improve our security."
Republican Senate majority leader Mitch McConnell also expressed concern, telling ABC's This Week the Government needs "to be careful".
He said the US should remember that some of the "best sources" in the war against terror were Muslims, both at home and abroad.
It came as further protests, including one in Washington DC, took place across the US in protest at the order.