Republican presidential nominee Donald Trump has warned countries like France that he says are compromised by terrorism may be subjected to the "extreme vetting" he proposes to deter attacks in the US.
When asked if his proposal might lead to a point when few people from overseas are allowed into the US, Mr Trump said: "Maybe we get to that point".
He added, in the interview to air on Sunday on NBC's Meet The Press: "We have to be smart and we have to be vigilant and we have to be strong."
For months Mr Trump has called for a temporary ban on foreign Muslims seeking to enter the United States and criticised the Obama administration for continuing to admit refugees from Syria.
He returned to the idea in his speech on Thursday night at the Republican National Convention in Cleveland, Ohio.
Mr Trump said the US "must immediately suspend immigration from any nation that has been compromised by terrorism until such time as proven vetting mechanisms have been put in place" - notably leaving out any reference to Muslims or to Syria, Iraq and other Middle East nations.
In the NBC interview, Mr Trump noted "specific problems" in Germany and France - both countries have been rocked by fatal attacks in public places in recent weeks.
Meet The Press host Chuck Todd asked if his proposal would limit immigration from France, adding: "They've been compromised by terrorism."
Mr Trump replied: "They have totally been. And you know why? It's their own fault. Because they allowed people to come into their territory."
He then called for "extreme vetting" and said: "We have to have tough, we're going to have tough standards. If a person can't prove what they have to be able to prove, they're not coming into this country."
During his interview, Mr Trump also took issue with descriptions of his convention speech as "dark".
He said: ''It was an optimistic speech."
Referring to his mentions of crime as well as shootings and terrorist attacks both here and overseas, he said, "Sure, I talk about the problems, but we're going to solve the problems."
The White House candidate also defended Roger Ailes, the founder of US TV network Fox News, who has resigned amid accusations of sexual harassment by numerous women.
Mr Trump described Mr Ailes as a long-time friend and said "some of the women" complaining about him had been helped by him in the past and earlier had said good things about him.
"It's very sad," Mr Trump said. "Because he's a very good person. I've always found him to be just a very, very good person."