"Allowing people who are from a country that has a propensity to do us harm, [we need] to make sure that we take the necessary steps, to ensure that the people who come to this country, especially areas that have a higher degree of concern, that we take the appropriate steps to make sure that they're coming to this country for all the right reasons."
Syria's six year civil war has forced more than 11 million people to uproot, according to recent estimates. The resulting refugee crisis has overwhelmed countries throughout the Middle East and Europe.
Observers have suggested that establishing the type of safe zones Trump is proposing could require tens of thousands of American troops, possibly drawing the U.S. into another extended overseas military conflict.
There are about 500 American troops on the ground now in Syria, mostly special operations personnel advising local militias and Turkish military forces battling the Islamic State. U.S. officials acknowledged earlier this month that the relatively light U.S. footprint in Syria also includes forward air controllers, who help to coordinate coalition airstrikes.
Another 5,000 troops are deployed to neighboring Iraq, also in advising and assistance roles.
It's unclear how Mattis and the Pentagon feel about Trump's plan, though the military brass is surely mindful of the challenges inherent to sending large numbers of troops into such a violent, unstable region. Some leaders, including the Marines' top general, have said previously that deploying American forces into Syria could be risky, especially if the mission is open-ended.
"I don't want to stay in Raqqa," Gen. Robert Neller told a roomful of Marines in November 2015, referencing the Islamic State's self declared capital in Syria. "There's nothing there that I want."
Such an effort could prove unpopular among many rank-and-file troops, too. Most are deeply skeptical of past nation-building missions overseas, namely in Iraq and Afghanistan. A September poll of 2,200 active-duty troopsfound that about 55 percent said they "strongly oppose" or "somewhat oppose" such efforts.
Several leading national security experts also have cautioned about the perceived over reliance on the military to conduct missions that don't fit its traditional portfolio.
Another potential hurdle: Trump's plan would require some level of coordination with Russia, since its military is currently operating in portions of Syria in what they insist are counter-terrorism operations. Though Mattis and other key figures in Trump's administration have said that Russia is not to be trusted, Trump has signaled that he's open to cooperating with Moscow in the war on ISIS.
The draft executive order proposes a dramatic overhaul of U.S. refugee admissions program, including new procedures "to determine what additional procedures can be taken to ensure those approved for refugee admission do not pose a threat."
It also calls for an immediate 30-day suspension of all visas to travelers from countries with terrorist influences that "would be detrimental to the interests of the United States."
Andrew deGrandpre is Military Times' senior editor and Pentagon bureau chief. On Twitter: @adegrandpre. Leo Shane III covers the White House and Congress. On Twitter: @LeoShane. Military Times senior writer Jeff Schogol contributed to this report. On Twitter: @JeffSchogol
Leo covers Congress, Veterans Affairs and the White House for Military Times. He has covered Washington, D.C. since 2004, focusing on military personnel and veterans policies. His work has earned numerous honors, including a 2009 Polk award, a 2010 National Headliner Award, the IAVA Leadership in Journalism award and the VFW News Media award.