Protests are continuing outside several airports across the US and around the world following the implementation of President Trump's measures.
Thousands have been expressing their anger at the 90-day ban and the suspension of refugee resettlement for 120 days.
Former US president Barack Obama has voiced his support for those demonstrating.
A spokesman for Mr Obama says he is heartened by the level of engagement in communities around the country.
He adds that citizens exercising their Constitutional right to assemble, organise and have their voices heard by their elected officials is what is expected when American values are at stake.
Muslim leaders in the US have also filed a broad lawsuit against the measures on constitutional grounds.
Shereef Akeel, from the Council on American Islamic Relations, describes the actions as unprecedented.
"Make no mistake: our First Amendment was attacked last week at its fundamental core and it's unprecedented what has occurred. For the first time, there's a broad proclamation that our country has issued an edict that it prefers one religion over another. That would make our founding fathers roll in their graves because that's the whole reason why they came here to America -- to escape religious persecution."
In Washington state, the Attorney General has also filed a lawsuit questioning the constitutionality of the measures.
Bob Ferguson is one of 16 state attorneys-general who released a statement over the weekend calling the ban "un-American and unlawful."
"We are a country based on the rule of law and in a courtroom it's not the loudest voice that prevails, it's the Constitution. That is why we are a nation of laws. At the end of the day you are either abiding by the Constitution or you are not and, in our view, the President is not adhering to the Constitution when it comes to his executive action. It is my responsibility as attorney general to defend the rule of law, to uphold the Constitution on behalf of the people of this state."
The order has also unleashed a global backlash, including from US allies, that view the actions as discriminatory and divisive.
Britain's Foreign Secretary, Boris Johnson, has reiterated the UK's stance on the ban.
"This is of course a highly controversial policy which has caused unease, and I repeat, that this is not an approach that this government would take."
But Donald Trump is pressing ahead with the measures.
Again taking to Twitter, Mr Trump says had he given warning before implementing the measures, "the bad" would have rushed into the US.
He added there are "a lot of bad dudes out there."
His White House spokesman, Sean Spicer, elaborated on the Presidemt's view the measures are necessary to protect Americans from acts of terror.
"His view in general is not to wait to get ahead of the curve. There wasn't a specific threat -- that you have to do this Saturday, Sunday. The point that I'm trying to make is that we don't know when that hour comes. We don't know when that individual crosses into our border to do us harm. And so, the idea of waiting when you don't know, could it be that night, could it be the next day, could it be the next week... The president's view is I'm not going to wait, I want to make sure that we protect the homeland as soon as possible with every measure that I can."