One key question for many is how the order will affect US green card holders and people who hold dual citizenship with a Trump approved country and one of the seven banned nations.
Adding to the confusion, Trump administration officials seemed to at times contradict themselves during appearances on Sunday news shows. In mere minutes during an interview with NBC, White House chief of staff Reince Priebus said the order "doesn't affect" green card holders, then later said "of course" it affects green card holders from Iran, Iraq, Syria, Sudan, Libya, Yemen and Somalia -- the seven countries Trump has temporarily stop immigration from for 90 days.
Trump on Sunday defended his recent executive order on extreme vetting, saying in a statement: "We will continue to show compassion to those fleeing oppression, but we will do while protecting our own citizens and voters."
He added: "This is not a Muslim ban, as the media is falsely reporting. This is not about religion -- this is about terror and keeping our country safe."
He said his first priority "will always be to protect and serve our country, but as President I will find ways to help all of those who are suffering."
But a top GOP senator, citing green card holders in particular, called on Trump to revise portions of the order.
"We all share a desire to protect the American people, but this executive order has been poorly implemented, especially with respect to green card holders," Senate Foreign Relations Chairman Bob Corker said Sunday. "The administration should immediately make appropriate revisions, and it is my hope that following a thorough review and implementation of security enhancements that many of these programs will be improved and reinstated."
Later Sunday, Homeland Security Secretary John Kelly issued a statement clarifying their status saying "lawful permanent resident status will be a dispositive factor in our case-by-case determinations."
Another Homeland Security official told CNN the green card holders who are returning to the US will still go through additional screening and national security checks upon landing. However, the government is trying to ease their entry back into the US. Unless they have a significant criminal history or links to terrorism, they will be allowed back in the country after going the check the official said.
"This is our message to them: get on a plane. Come back to the US. You will be subject to secondary screening, but everything else will be normal," the Homeland Security official told CNN.
A White House official said Sunday more than 170 green card holders had been waived in as of 3 p.m.
Here is what we know about how Trump's order impacts green card holders and dual citizens:
Where do green card holders from Trump's seven banned countries stand?
Senior officials at the Department of Homeland Security initially interpreted Trump's order to not apply to green card holders from the seven banned countries. Trump White House overruled that reading, however, meaning those green card holders were initially barred.
But a federal judge in New York temporarily blocked part of Trump's order late on Saturday night, ruling that citizens of the seven countries who hold valid visas and have already arrived in the United States cannot be removed from the United States.
A senior Department of Homeland Security official told CNN on Saturday that the United States denied entry to 109 travelers who were in transit at the time Trump signed the order. Some of those residents of Iran, Iraq, Sudan, Syria, Somalia, Libya or Yemen were detained at airports across the country this weekend, leading to large protests at major airports.
The official added that no legal green card holders have been denied entry, but Trump's order has made it more difficult to enter the United States.
Here is the process for US green card holders from Iran, Iraq, Sudan, Syria, Somalia, Libya or Yemen as CNN understands it now: They are allowed to board their plane and fly to the United States. Once they land, their fingerprints and other information will be collected and they will be subject to a secondary interview, in part, to judge whether the traveler is a national security risk.
Priebus said Sunday that border agents have "discretionary authority" to question travelers from certain countries.
And a White House official told CNN Sunday that the ruling "does not undercut the President's executive order."
"All stopped visas will remain stopped. All halted admissions will remain halted. All restricted travel will remain prohibited," the official said. "The executive order is a vital action toward strengthening America's borders, and therefore sovereignty. The order remains in place."
There was no buffer time to Trump's order, meaning that it effectively went into order as soon as the President signed it. The order, however, was not publicly released for hours after Trump's pen hit paper, leading airlines and other stakeholders to grow confused about how they implement the new rules.
Two days since the order has been signed, airlines have begun instructing travelers that permanent green card holders are allowed to travel to the United States.
The International Air Transport Association told airlines on Sunday that the Custom and Border Patrol instructed them that "lawful permanent residents of the United States (green card holders) were out of scope of the (executive order)," according to an email obtained by CNN.
What if you are a dual citizen from one of Trump's seven banned countries?
The situation is similar for people from Trump's seven banned countries who also hold valid passports from Trump approved countries: confusion reigns.
Initially, the guidance provided by a State Department official was that someone who holds dual citizenship from one of the seven banned countries would be barred from entering the United States.
"Travelers who have nationality or dual nationality of one of these countries will not be permitted for 90 days to enter the United States or be issued an immigrant or non-immigrant visa," a State Department official said Saturday. "Those nationals or dual nationals holding valid immigrant or non-immigrant visas will not be permitted to enter the United States during this period."
This guidance means that a Iranian national who also holders a Canadian passport would be barred from entering the United States.
The same State Department official told CNN that the executive order "should not affect dual-national Americans at all," meaning a US citizen who also holds citizenship from one of Trump's seven banned countries would be allowed in.
But in the last 24 hours, the guidance has seemingly changed.
The International Air Transport Association told their airlines that dual nationals who hold a passport from an approved country would be allowed in.
"Dual nationals holding and traveling with a valid passport issued by a State other than one of the above-mentioned will be allowed entry provided meeting all criteria based upon the passenger's nationality," their guidance reads.
The confusion, however, has led many companies and institutions to caution anyone with citizenship or ties to one of the seven banned countries from leaving the United States.
Representative from Google, for example, told employees who are dual nationals from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen to stay in the United States before more clarity could be provided.
Did Trump's banned countries list really originate with Obama?
The Trump administration's explanation is that they started with countries already designated by the Obama administration
, and more can be added. But there is a difference between what Obama did and what Trump is doing. It comes down to the scope and breadth of people impacted, at least for the start.
Trump's action says they will implement this temporary ban while they figure out how to give people from these countries increased scrutiny. For now it is an almost complete ban.
The Obama administration's travel restriction provided extra scrutiny to people who traveled to these seven countries -- Iran, Iraq, Sudan, Syria, Somalia, Libya and Yemen -- because they are hotbeds for foreign fighters. It did not specifically ban people from entering the US just because they were citizens from these seven countries. All were still eligible to apply and get interviewed, they just could not utilize the visa waiver program. It was not a complete ban.
The countries are indeed from the Obama administration's list, but the breadth of the limitations are far greater at the outset.
It also does not explain why other countries are not on the list. There are suggestions in the Trump administration officials' comments that the list could expand. That remains to be seen.