Donald Trump said Sunday he would subject people from France, among other countries, to "extreme vetting" as they seek to enter the United States, a move he says is necessary to deter terror attacks.

The GOP presidential nominee, in an interview that aired Sunday on NBC's "Meet the Press," was asked if his proposal might mean that ultimately far fewer people from overseas would be allowed into the U.S.

"Maybe we get to that point," Trump replied, adding: "We have to be smart and we have to be vigilant and we have to be strong."

In the interview, Trump also rejected suggestions that his stance on requiring NATO members to pay their share was a mistake; dismissed descriptions of his nomination acceptance speech as "dark," instead calling it "optimistic"; and expressed disapproval of David Duke, the former Ku Klux Klan leader who is seeking a Senate seat from Louisiana.

Trump reiterated that he wouldn't release his tax returns until an IRS audit is complete, although such an inquiry doesn't bar him from making the documents public. Trump also said he believes 2012 GOP nominee Mitt Romney lost the election because of a public scrutiny of his taxes.

For months Trump has called for a temporary ban on foreign Muslims seeking to enter the United States and criticized the Obama administration for continuing to admit refugees from Syria.

In his speech Thursday night at the Republican National Convention, he said the U.S. "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 Mideast nations.

In the NBC interview, Trump noted "specific problems" in Germany and France and "Meet the Press" host Chuck Todd asked if his proposal would limit immigration from France. "They've been compromised by terrorism," Todd said.

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."

He also took issue with descriptions of his convention speech earlier in the week as "dark." `'It was an optimistic speech," Trump said. Referring to his mention 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."

And he criticized Duke, who cited Trump's campaign as an inspiration for his Senate bid. Trump was quick to say he rejected efforts by Duke to run for the Senate. In an interview several months ago, Trump was asked about Duke offering his support and Trump responded: "I don't know anything about David Duke." His initial response drew harsh criticism from Democrats, Republicans and civil rights groups," and he later said "I disavow" Duke's support. 

The Associated Press contributed to this report.