Trump denies restriction is 'a Muslim ban'

US President Donald Trump is vigorously defending his immigration restrictions, as protests spread throughout the country, saying "this is about terror and keeping our country safe."

"To be clear, this is not a Muslim ban, as the media is falsely reporting," Trump said in a statement.

"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 Sunday, a senior administration official declared the order's implementation "a massive success story," claiming it had been done "seamlessly and with extraordinary professionalism."

That, despite widespread confusion and an apparent walk-back about how the order, which temporarily bars the citizens of seven majority Muslim nations from entering the US., would be applied to certain groups, like US legal permanent residents.

Homeland Security Secretary John Kelly issued a statement Sunday saying that, absent 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 US, as officials had previously said. It remains unclear what kind of additional screening they will now face.

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.

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.

Top congressional Republicans, meanwhile, were backing Trump despite concerns raised Sunday from a handful of GOP lawmakers and condemnation from the Koch political network, which is among the most influential players in the conservative movement.

Republican senators John McCain and Lindsey Graham warned of unintended consequences, expressing fear the order could "become a self-inflicted wound in the fight against terrorism."