A senior US administration official has hailed the implementation of a temporary travel ban on people from seven mainly Muslim countries as a “massive success story”.
The official said it had been implemented “seamlessly and with extraordinary professionalism”.
“It really is a massive success story in terms of implementation on every single level,” the official said.
On Friday, Mr Trump signed an executive order suspending travel to the US from Syria, Iraq, Iran, Yemen, Somalia, Sudan and Libya. He said it was to protect Americans from terrorism on home soil.
But there has been criticism of the ban from some top Republicans, anger from the mainly Muslim countries affected, widespread protests and confusion at US airports.
Judges in at least five American states have also blocked federal authorities from enforcing the order.
And thousands of academics, including 13 Nobel Laureates, signed a petition protesting Mr Trump’s order.
Senior Republican Senator John McCain said the President’s order had been “confusing”, adding fears that the order would “become a self-inflicted wound in the fight against terrorism”.
Senator Bob Corker, Republican chairman of the Senate Foreign Relations Committee and a Trump supporter, said the order had been poorly implemented, especially for green card holders.
He said the administration should “immediately made appropriate revisions”.
Senate Minority Leader Chuck Schumer, a Democrat, teared up on camera as he described the ban as “mean-spirited and un-American”.
New York police estimated that 10,000 people protested in Battery Park, just across across the river from the Statue of Liberty – a symbol of freedom and immigration.
Thousands of people also gathered outside the White House, while others demonstrated at airports around the country.
There are also protests planned in the UK.
The Arab League chief voiced “deep concern” about the ban, while the Iraqi parliament’s foreign affairs committee said in a statement: “Iraq is in the front line of the war on terrorism… and it is unfair that the Iraqis are treated in this way.”
Some in Iraq, including hardline Shia representatives, demanded the Iraqi PM expel US citizens in retaliation.
Senior politicians in several European countries also criticised the order, including German Chancellor Angela Merkel and the French and Swiss foreign ministers.
But Mr Trump has defended the ban, saying: “The seven countries named in the executive order are the same countries previously identified by the Obama administration as sources of terror.
“To be clear, 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.
“There are over 40 different countries worldwide that are majority Muslim that are not affected by this order.
“We will again be issuing visas to all countries once we are sure we have reviewed and implemented the most secure policies over the next 90 days.”