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.”

Trump released a statement asserting, “To be clear, this is not a Muslim ban, as the media is falsely reporting.”

The president addressed the issue late Sunday in a statement as some Republicans in Congress - including Ohio's Sen. Rob Portman - urged caution amid legal challenges to the order banning travellers from seven predominantly Muslim countries. Top congressional Republicans have largely remained behind Trump on the issue.

“America is a proud nation of immigrants and we will continue to show compassion to those fleeing oppression,” Trump said, “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,” he said. “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. Many have accused the administration of rushing to implement the changes, resulting in panic and confusion at the nation's airports.

“You have an extreme vetting proposal that didn't get the vetting it should have had,” said Portman, who urged the new president to “slow down” and work with lawmakers on how best to tighten screening for foreigners who enter the United States.

“In my view, we ought to all take a deep breath and come up with something that makes sense for our national security” and reflects the fact that “America's always been a welcoming home for refugees and immigrants,” he said.

White House press secretary Sean Spicer on Monday morning defended the closed-mouth discussions that preceded Friday's announcement, saying that “I think there are some people who might not like the way it was done, but they were all consulted in the process.”

Interviewed on MSNBC's Morning Joe, Spicer said officials put the safety of the American people first and said officials didn't want to “telegraph” what they were going to do. He acknowledged “the secret way we had to roll this out” and said that it was because of “security reasons.”

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.

But it's unclear whether the order will accomplish that. The order does not address homegrown extremists already in America, a primary concern of federal law enforcement officials. And the list of countries in Trump's order doesn't include Saudi Arabia, where most of the Sept. 11 hijackers were from.

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 Sunday the court ruling would not affect the overall implementation of the White House order.

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

“This executive order sends a signal, intended or not, that America does not want Muslims coming into our country. That is why we fear this executive order may do more to help terrorist recruitment than improve our security,” they wrote.

Trump fired back on Twitter, calling the pair “sadly weak on immigration.”