"We're going to declare war against ISIS. We have to wipe out ISIS," Trump said in the interview with CBS' Lesley Stahl, which aired on "60 Minutes" Sunday night.
"I am going to have very few troops on the ground. We're going to have unbelievable intelligence, which we need; which, right now, we don't have. We don't have the people over there," he said.
Trump added: "We're going to have surrounding states and, very importantly, get NATO involved because we support NATO far more than we should, frankly, because you have a lot of countries that aren't doing what they're supposed to be doing. We have to wipe out ISIS."
The interview -- featuring Trump and Pence side-by-side for the first time -- comes the week the Republican National Convention in Cleveland is set to nominate the two to face Hillary Clinton in the general election.
Trump tweeted on Sunday, "We are TRYING to fight ISIS, and now our own people are killing our police. Our country is divided and out of control. The world is watching."
Trump also laid the blame for the rise of ISIS at the feet of Clinton -- who was President Barack Obama's secretary of state during his first four years in office.
"Hillary Clinton invented ISIS with her stupid policies. She is responsible for ISIS. She led Barack Obama -- because I don't think he knew anything; I think he relied on her," Trump said. "As Bernie Sanders said, 'Her judgment is so bad.' She's got bad judgment. She's got bad instincts."
Pence criticized Obama and Clinton, saying the two have "led from behind."
"The larger issue here is declining American power in the world," he said. "I truly do believe that history teaches that weakness arouses evil. And whether it be the horrific attack in France, the inspired attacks here in the United States, the instability in Turkey that led to a coup -- I think that is all a result of a foreign policy of Hillary Clinton and Barack Obama that has led from behind and that has sent an inexact, unclear message, about American resolve."
Picking a running mate
In the interview, Trump also said he didn't expect Pence to campaign in a similar manner to his brash, confrontational style.
"We're different people," Trump said. "I understand that."
Pence also said he would be comfortable disagreeing with Trump.
"I promise you that when the circumstances arise where I have a difference on policy or on presentation ... I would have no hesitation, were I privileged to be Vice President, to walk into the President's office, close the door, and share my heart," Pence said. "And I also know this good man would listen, and has -- and has the leadership qualities to draw from the people around him."
Trump also gave more insight into how he made up his mind in picking Pence, saying "a lot of people" were campaigning to him for the job.
"(People) that called me and came to me and wanted it badly," Trump said. "And you know, the press didn't report that. The press said, 'Well, maybe he's having a hard time picking.'"
The mogul said he brought up the idea to Pence, saying he got to know the governor during the Indiana primary. Pence endorsed Texas Sen. Ted Cruz ahead of that race.
"I did very well in Indiana, like I did just about everywhere else in all fairness," Trump said. "I got to know him very well and I gained great respect for him. And I looked at the numbers. ... Unemployment? What a great job he did. Jobs? What a great job he did. Triple-A rating on his bonds."
Trump said Pence thought about being considered for "about two seconds" before calling back and saying he was interested. He said he picked Pence not to win Indiana, which he expected to win anyway, but for his individual "quality."
"I'm an outsider. I am a person that used to be establishment when I'd give them hundreds of thousands of dollars. But when I decided to run, I became very anti-establishment because I understand the system," Trump said. "He's very establishment, in many ways, and that's not a bad thing. ... He has helped bring the party together."
The interview also highlighted plenty of areas the two candidates diverge.
On trade, the Iraq War, preventing foreign Muslims from entering the country temporarily, and waterboarding, Pence and Trump were pressed on the divergence in their past positions.
Pence did his best to present a united front.
"I don't think we should ever tell our enemy what our tactics are," Pence said when pressed on Trump's support of waterboarding, for example. "What I'm okay with is protecting the American people."
On his vote in favor of the Iraq War, Trump said he'd let that slide.
"Many people have, and frankly, I'm one of the few that was right on Iraq," Trump said. "He's entitled to make a mistake every once in a while."
But he stuck by his criticism of Clinton for the same reason: "But she's not."
Proposed Muslim ban explained
In the interview Trump also explained for the first time in his own words where he now stands on the Muslim ban he proposed in December.
Trump's aides have suggested that he has modified his proposal from a "total and complete shutdown of Muslims entering the United States," to only banning individuals from terror states.
Trump was most recently asked about this in Scotland where he wasn't specific on where exactly he stood on the issue.
In the interview Trump said he doesn't intend to ban all Muslims, but instead from certain countries.
"There are territories and terror states and terror nations that we're not going to allow the people to come into our country. And we're going to have a thing called 'extreme vetting.'"