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In an exclusive interview on Fox News' "Tucker Carlson Tonight," Vice President Mike Pence on Thursday night affirmed that the White House would reject any Democratic spending bill without funding for a border wall.

The vice president added that President Trump "is in the process of evaluating" whether to remove troops from Afghanistan, and vowed that the military's withdrawal from Syria will be conducted in an "orderly fashion."

Pence's comments came as the new House majority, which was sworn in earlier Thursday, debated an interim, stopgap spending bill to fund the Department of Homeland Security through Feb. 8. The bill, which was ultimately approved late Thursday by a 239 to 192 vote, does not include any new wall money, and Senate Republicans and the White House have both described it as a non-starter that will never become law. Five Republicans voted for the bill.

Another piece of legislation approved by the House late Thursday would fund six of the seven unresolved spending bills through Sept. 30. The bill was approved by a  241-190 vote at approximately 10 p.m. ET, with seven Republicans joining Democrats to vote yea. The measure, which the White House has also said will not become law, puts together six of the seven unresolved appropriations bills in one package.

"Democrats broke off negotiations about a week ago, but the president’s made it clear: We’re here to make a deal, but it’s a deal that’s going to result in achieving real gains on border security," Pence said. "And, you have no border security without a wall. We will have no deal without a wall.

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"What we’ve completely focused on is keeping the president’s promise, to build a wall, to pass legislation that provides other support for border security, that gives the people that are enforcing our laws at the border, and across the border -- enforcing our immigration laws, the resources and the tools that they need."

The vice president pointed to a compromise floated during a legislative showdown over the summer, which would have provided enhanced statutory protections to so-called "Dreamers," or illegal immigrants who entered the U.S. at a young age. The president had signaled support for the measure.

"There’s a lot of people talking about a lot of different ideas, you know frankly, the better part of a year ago, the president expressed a willingness to deal with the issue of Dreamers in a compassionate way," Pence said. "People who were brought here as children, and through no fault of their own -- he’s discussed that, it’s being talked about."

While U.S. authorities "actually saw a decline in illegal immigration and incursions on our southern border" in the early days of Trump's presidency, Pence said, "in the last 12 months we’ve literally seen a dramatic increase ... 2,000 people a day [are] apprehended at our border or found to be inadmissible, trying to enter our country."

The solution, Pence said, is a "barrier," along with "technology, drones, the kind of support that our border agents know will assist them in doing their job. But bottom line, if there’s no wall, there’s no deal."

"But bottom line: If there’s no wall, there’s no deal."

— Vice President Mike Pence

Separately, Pence suggested that Trump's planned pullout from Syria was appropriate because terrorists there have been defeated -- but, he added, the fight against the Islamic State terror network will continue.

"The reality is we have defeated ISIS, we have defeated the caliphate," Pence said. "And, what the president announced just before Christmas is not that we’re giving up on the fight of ISIS; we’re going to continue to lean into the fight on ISIS."

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Speaking to Fox News on Wednesday, Retired Army Col. Douglas MacGregor praised Trump's decision, saying U.S. overseas commitments have been a "disaster" for everyday Americans.

However, several top Republicans, including South Carolina Republican Sen. Lindsey Graham, have said Trump's initially planned 30-day pullout was too hasty. After speaking with Trump this week, Graham said that the president has agreed to slow the drawdown.

Asked whether Trump would similarly pursue an Afghanistan withdrawal, as he has reportedly been debating, Pence said only that the idea was under active consideration.

The potential maneuver would involve more than 3,000 U.S. troops getting pulled out, a senior U.S. official told Fox News in December. There are 15,000 troops currently on the ground in Afghanistan.

"Well, the president is in the process of evaluating that, as we speak," Pence said. "I was in Afghanistan last year. In his speech in August, President Trump, basically through new rules of engagement, new resources, additional military personnel, gave our folks on the ground the ability to take the fight, be at the tip of the spear, supporting the Afghan National Army in the battle against the Taliban, ISIS, Khorasan, Al Qaeda, re-emerging in Afghanistan."