White House officials clarified on Sunday that the order does not apply to certain people.
The action “doesn’t affect green card holders moving forward,” Priebus said on NBC’s “Meet the Press.”
What can states do?
The attorney generals of 15 states and the District of Columbia issued a joint statement Sunday condemning Trump's executive order as unconstitutional.
The Associated Press reported that the attorney generals said religious liberty has been a bedrock principle of the U.S. and that no president can change that truth.
Washington, California, New York, Pennsylvania, Massachusetts, Hawaii, Virginia, Oregon, Connecticut, Vermont, Illinois, New Mexico, Iowa, Maine and Maryland signed onto the statment.
The attorney generals also predicted Trump's order will be struck down.
What about detainees?
There was no exact number on Sunday on how many people were still detained in the U.S. as a result of Trump’s travel ban, according to lawyers with the American Civil Liberties Union.
The ACLU’s Immigrants’ Rights Project deputy director Lee Gelernt told reporters on Sunday that there was still confusion over the status of detainees and the new rules for entering the country, according to the Associated Press.
Gelernt said the ACLU is waiting for a list of detainee names from the government to try to determine who has been detained.
Trump said Saturday the order is "not a Muslim ban."
"It's working out very nicely," he said. "We're going to have a very, very strict ban and we're going to have extreme vetting, which we should have had in this country for many years."
Reaction to the ban
Reaction to the executive order has been swift and varied, from thousands of protesters across the U.S. to politicians and international governments.
The University of Notre Dame, among others, is calling on Trump to rescind the restrictions on refugees entering the U.S. The Rev. John Jenkins called Trump's action indiscriminate and abrupt and predicted it would diminish the country.
The executive order Trump signed on Friday suspends the U.S. refugee program for 120 days and barrs Syrians from entering the country indefinitely.
What is the "immigration ban?"
Any non-U.S. citizen from Iraq, Syria, Iran, Sudan, Libya, Somalia or Yemen is now barred from entering the United States.
Legal permanent residents -- green card and visa-holders -- from those seven countries who were out of the United States after Friday cannot return to the U.S. for 90 days.
>>Read the executive order
The order also singled out Syrians for the most aggressive ban, indefinitely blocking entry for anyone from that country, including those fleeing civil war.
The order also directed U.S. officials to review information as needed to fully vet foreigners asking to come to the U.S. and draft a list of countries that don't provide that information. That left open the possibility that citizens of other countries could also face a travel ban.
Are there exceptions?
There's an exemption for immigrants and legal permanent residents whose entry is in the U.S. national interest.
Visa and green card holders already in the U.S. will be allowed to stay. Foreign government, United Nations, international organization and NATO visas are also exempt.
The U.S. may still admit refugees on a case-by-case basis during the freeze. Also officials would continue to process requests from people claiming religious persecution "provided that the religion of the individual is a minority religion in the individual's country."
What happened to travelers as the order took effect?
The immediate fallout from Trump's order meant that an untold number of foreign-born U.S. residents now traveling outside the U.S. could be stuck overseas for at least 90 days — despite holding permanent residency "green cards" or other visas.
Foreign nationals who were allowed to board flights before the order was signed Friday were being detained at U.S. airports and told they were no longer welcome.
>>Read Protests erupt in response to Trump's executive order on immigration
This has prompted protests online and at John F. Kennedy International Airport in New York where a crowd of protesters grew Saturday as word got out that up to a dozen travelers had been detained in connection with the executive order.
The Associated Press contributed to this report.