Reince Priebus, Trump's chief of staff, said on NBC's "Meet the Press"
that "as far as green card holders moving forward, it doesn't affect them."
However, he later added: "If you're traveling back and forth you're going to be subjected to further screening."
Green card holders from the seven banned countries, when they land, will undergo additional security screening, including an interview and having their fingerprints checked, sources told CNN. If there are no red flags, then they would be allowed entry.
A White House official said Sunday more than 170 green card holders had been waived in as of 3 p.m.
"There is discretionary authority that a Customs and Border Patrol agent has when they suspect that someone is up to no good when they travel back and forth to Libya or Yemen," Priebus said.
Priebus' comments come in the wake of a judge issuing a stay blocking the deportation of those affected by Trump's executive order blocking foreigners from seven countries -- including refugees -- from entering the United States.
The order led to protests at airports across the United States and controversy over whether people who had lived and worked in the country for years would be allowed to return from trips overseas. Some were still being detained Sunday morning.
Senate Minority Leader Chuck Schumer, D-New York, tweeted Sunday that he had spoken with Homeland Security Secretary John Kelly.
"All those still in airports expected to be admitted," Schumer tweeted.
Kellyanne Conway, a Trump adviser, also said Sunday those currently detained who are not deemed threats would be released.
"I am told by the officials that anyone who's being detained, if there's no further threat, if they're not dangers to this country, they can expect to be released in due course -- as most of them have already," she said on "Fox News Sunday."
"If they are not dangerous, if they're not a threat, then they will be disposed of on a case-by-case -- their situations will be handled on a case-by-case basis," she said.
Later Sunday, Homeland Security Secretary John Kelly issued a statement clarifying that "lawful permanent resident status will be a dispositive factor in our case-by-case determinations."
Another Homeland Security official told CNN the green card holders who are returning to the US will still go through additional screening and national security checks upon landing. However, the government is trying to ease their entry back into the US. Unless they have a significant criminal history or links to terrorism, they will be allowed back in the country after going the check the official said.
"This is our message to them: get on a plane. Come back to the US. You will be subject to secondary screening, but everything else will be normal," the Homeland Security official told CNN.