Protests against right-wing US President Donald Trump's ban on refugees and immigrants from several Muslim-majority countries have been held in cities across the US, including in New York City and Washington, DC.

In the US capital, thousands gathered outside the White House, while more than 1 000 protesters assembled in New York City's Battery Park to demonstrate against Trump's executive order, which places harsh restrictions on immigration from seven Muslim-majority countries.

More protests are slated to take place in Baltimore, Atlanta, Austin, Dallas, Boston, Boise, Chicago, Detroit, San Francisco and other cities across the country.

A day earlier, thousands of protesters amassed at airports across the country as news spread that immigrants and travellers were being detained there. Among those detained were legal residents who carry US green cards.

Demonstrators only dispersed when a federal judge blocked part of Trump's executive order on immigration, ruling that travellers who have already landed in the US with valid visas should not be sent back to their home countries.

Lawyers had filed a legal case in response to the order that includes a 90-day entry ban on citizens of Syria, Iraq, Somalia, Sudan, Iran, Libya and Yemen.

US District Judge Ann Donnelly's ruling late on Saturday concerns dozens of people who were detained at airports following Trump's actions. The total number of people detained was unclear.

The American Civil Liberties Union (ACLU), which had filed a class action lawsuit against the ban, hailed the temporary stay of execution as a victory.

"This ruling preserves the status quo and ensures that people who have been granted permission to be in this country are not illegally removed off US soil," Lee Gelernt, deputy director of the ACLU's Immigrants' Rights Project, said.

Some reports said immigration authorities were still implementing the ban sporadically in a number of airports.

Politicians, officials speak out

Attorney generals from 16 US states - including California, New York and Pennsylvania - issued a joint statement on Sunday condemning Trump's move.

"We are committed to working to ensure that as few people as possible suffer from the chaotic situation that it has created," the statement said.

US senators John McCain and Lindsey Graham, both from Trump's Republican Party, said on Sunday that the president's order may do more to help recruit "terrorists" than improve US security.

"Ultimately, we fear this executive order will become a self-inflicted wound in the fight against terrorism," they said in a statement, adding that the US should not stop green card holders "from returning to the country they call home.

"This executive order sends a signal, intended or not, that America does not want Muslims coming into our country. That is why we fear this executive order may do more to help terrorist recruitment than improve our security," said McCain, of Arizona, and Graham, of South Carolina.

The top Democrat in the US Senate said on Sunday he will push legislation to undo the discriminatory ban.

Senator Chuck Schumer called the executive order "mean-spirited and un-American" and said it must be reversed immediately.

Amid growing global criticism, outrage from civil rights groups and legal challenges, Trump defended the ban on Sunday.

He and senior aides sought to defend the policy and play down the chaos sparked by Friday's order. But confusion persisted over details of implementation, in particular for green card holders who are legal residents of the US.

"Our country needs strong borders and extreme vetting, NOW. Look what is happening all over Europe and, indeed, the world - a horrible mess!" Trump wrote on Twitter on Sunday.