"I think it's regrettable there was some confusion in the rollout of this," the House speaker from Wisconsin said, citing the detention of some lawful permanent residents.
Late Friday, Trump signed the order, which indefinitely bars Syrian refugees from entering the U.S. It also suspends all refugee admissions for 120 days and blocks citizens of seven Muslim-majority countries from entering the country for 90 days.
Reports since have indicated that government agencies, including the secretaries of Defense and Homeland Security, knew little about the order's specifics before Trump signed it. Confusion ensued at airports as some green card holders and an Iraqi who helped American military efforts were detained at U.S. airports.
Ryan said that Homeland Security Secretary John Kelly, who will hold a news conference at noon ET about the order, will make sure it runs more smoothly moving forward.
"Clearly none of us want to see people with green cards get implicated in this," Ryan said.
Protests erupted around the country after Trump's order, and some lawmakers on both sides of the aisle opposed it. In particular, they focused on the potential that it could energize terrorists rather than harm them.
Ryan noted that "the rhetoric surrounding this could be used as a recruiting tool and I think that's dangerous." However, he defended the policy's intentions, saying, "We need the pause and we need to make sure that the vetting standards are up to snuff."
Late Monday, Trump fired acting U.S. Attorney General Sally Yates, who defied the White House and refused to defend the order. Trump called her move a "betrayal."