US President Donald Trump has vigorously defended his immigration restrictions, saying "this is about terror and keeping our country safe".
n a statement, Mr Trump said: "To be clear, this is not a Muslim ban, as the media is falsely reporting."
The president addressed the issue late on Sunday as some Republicans in Congress urged caution amid legal challenges to the order banning travellers from seven predominantly Muslim countries.
Top congressional Republicans have largely remained behind Mr Trump on the issue.
Mr Trump added: "America is a proud nation of immigrants and we will continue to show compassion to those fleeing oppression, but we will do so while protecting our own citizens and border.
"This is not about religion - this is about terror and keeping our country safe.
"I have tremendous feeling for the people involved in this horrific humanitarian crisis in Syria.
"My first priority will always be to protect and serve our country, but as President I will find ways to help those who are suffering."
In a background call with reporters on Sunday, a senior administration official declared the order's implementation "a massive success story," claiming it had been done "seamlessly and with extraordinary professionalism".
Homeland Security Secretary John Kelly issued a statement on Sunday saying that, in the absence of information indicating a serious threat to public safety and welfare, residency would be a "dispositive factor in our case-by-case determination".
That means citizens of the seven countries who hold permanent US residency "green cards" will not be barred from re-entering the country, as officials had previously said.
It remains unclear what kind of additional screening they will now face.
Mr Trump's order, which also suspends refugee admissions for 120 days and indefinitely bars the processing of refugees from Syria, has sparked widespread protests and denunciations from Democrats and a handful of Republicans.
Many have accused the administration of rushing to implement the changes, resulting in panic and confusion at the nation's airports.
Protests were held at a number of airports across the US against the measure, including in Chicago, Detroit and Washington DC.
Several Democrats in Congress said they would be introducing legislation to stop the ban.
White House adviser Kellyanne Conway said the changes were "a small price to pay" to keep the nation safe.
The developments came a day after a federal judge in New York issued an emergency order temporarily barring the US from deporting people from the seven majority Muslim nations subject to Trump's 90-day travel ban.
The order barred US border agents from removing anyone who arrived in the US with a valid visa from Iraq, Syria, Iran, Sudan, Libya, Somalia and Yemen. It also covered anyone with an approved refugee application.
The Department of Homeland Security said the court ruling would not affect the overall implementation of the White House order.