Donald Trump is defending his immigration curbs in the face of a growing international backlash and legal challenges within the United States.
Many world leaders are speaking out against his order, while in the US, civil rights and faith groups, activists and Democratic politicians have promised to fight it. Federal judges have issued rulings barring authorities from deporting travellers affected by the executive order.
On Friday Mr Trump put a 120-day hold on allowing refugees into the country, an indefinite ban on refugees from Syria and a 90-day bar on citizens from seven predominantly Muslim countries: Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.
Over the weekend the president and senior aides sought to defend the policy and play down the chaos sparked by the order. "Our country needs strong borders and extreme vetting, NOW. Look what is happening all over Europe and, indeed, the world - a horrible mess!" Mr Trump wrote on Twitter on Sunday.
But confusion persisted over details of implementation, in particular for green card holders who are legal residents of the United States.
Democratic attorneys general from California and New York are among states discussing whether to legally challenge the order, according to officials.
A lawsuit brought by states would heighten the legal stakes surrounding the president's executive order, signed late Friday, as courtroom challenges to the ban have so far mostly been filed by individuals.
California and New York joined Pennsylvania, Washington and Hawaii in evaluating what specific claims could be filed, and in which court.
Federal judges in three states followed a US judge in New York in barring authorities from deporting travellers affected by Mr Trump's executive order.
Judges in Massachusetts, Virginia and Washington issued rulings late Saturday or early Sunday.
The federal judge in New York said stranded travellers could stay in the country. The American Civil Liberties Union, which sought the emergency court order, said it would help 100 to 200 people with valid visas or refugee status who found themselves detained in transit or at US airports.
The Department of Homeland Security said it would comply with judicial orders but that Mr Trump's immigration restrictions remained in effect.
The department said the US government retained its right to revoke visas at any time if required for national security or public safety.
Senate Democrat leader demands reversal of immigration order
Senate Democratic Leader Chuck Schumer demanded that Mr Trump reverse the executive order on immigration saying it made the United States appear "less humanitarian, less safe, less American".
"It must be reversed immediately, and Democrats are going to introduce legislation to overturn it," Mr Schumer said in New York.
Mr Schumer also said he had been told by US Homeland Security Secretary John Kelly that 42 people now detained at US airports would be processed and allowed to enter the country under a court order issued on Saturday night.
He said Mr Kelly also told him Trump's executive order would not affect green card holders, which contradicts previous administration statements.
Leading Republican Senator John McCain said the order had been confusing and raised a number of questions.
Mr McCain, chair of the Senate Armed Services Committee, is asking why the countries targeted by the order included Iraq, where US forces were fighting alongside Iraqi forces against the jihadists.