"This is nothing new. President Trump talked about this throughout the campaign and throughout the transition," White House Press Secretary Sean Spicer told ABC News.
"Protecting this nation and our people is the number one priority of this president and our government," Spicer said in a defence of the executive orders signed by Trump earlier this week which calls for temporary ban on nationals from seven predominantly Muslim countries from entering the US.
Spicer said the countries were first flagged as "countries of particular concern" by the previous administration of Barack Obama. "They should be asked certain questions. They should go through certain vetting," Spicer said.
The White House also pushed back on the argument that the executive orders literally means a ban on Muslims.
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"These seven countries, what about the 46 majority Muslim countries that are not included. Right there, it totally undercuts this nonsense that this is a Muslim ban," White House counselor Kellyanne Conway told Fox News separately.
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In a statement, Flake called the order unacceptable.
"President Trump and his administration are right to be concerned about national security, but it's unacceptable when even legal permanent residents are being detained or turned away at airports and ports of entry," he said.
"Enhancing long term national security requires that we have a clear-eyed view of radical Islamic terrorism without ascribing radical Islamic terrorist views to all Muslims," Flake said.
American Civil Liberties Union (ACLU) National said on Twitter "If you know someone entering country, tell them not to sign anything before talking to lawyer."
Appearing on CNN, Senator Rob Portman said the travel ban imposed on people from seven countries were identified by the previous administration. "I think the previous homeland security secretary had named those countries because of a lack of information and the fact that either ISIS or al Qaeda was present in those countries," he said.
"In fact, we are more welcoming than any country in the world, and we should continue to do so," Portman said.