More American politicians and celebrities are pledging to register in President Donald Trump's promised Muslim database, to protest and frustrate a policy many view as Islamophobic.

Former Secretary of State Madeleine Albright has added her voice to those of feminist icon Gloria Steinem, actress Mayim Bialik and activist Jonathan Greenblatt, writing on Twitter: "I was raised Catholic, became Episcopalian & found out later my family was Jewish. I stand ready to register as Muslim in #solidarity." All four are Jewish or have Jewish heritage.

But Rabia Chaudry, the Serial immigration attorney and author, has questioned the utility of these pledges: "For those who are well-intentioned and say they will register with Muslims, it did not work like that back then [under George Bush's failed NSEERS registry programme], and it will not now," she wrote.

Madeleine Albright's stand comes as the White House orders a halt on immigration from Muslim-majority countries Iran, Syria, Sudan, Yemen and Iraq, with whom America is currently allied in the fight to retake Mosul from Isis.

His Cabinet will also have the power to add countries to this list, raising fears that ordinary citizens of more countries – such as China – will also be banned.

President Trump's exact position on the Muslim registry remains opaque.

The seed of the idea was apparently planted by a reporter's question, who asked "is there going to be a database that tracks the Muslims here in this country?"

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"There should be a lot of systems, beyond database, we should have a lot of systems, and today you can do it," the President replied, speaking in November 2015 when he was still one of several in the race for the Republican nomination.

But when asked specifically about a database, he continued: "I would certainly implement that." Asked how such a database could work in practice, he simply replied "good management."

He has since variously said that "I certainly wouldn't want to do it but we have to be vigilant," and later claimed "I didn't say that. I never said that."

Carl Higbie, a former Navy SEAL and spokesperson for the Great America PAC for Donald Trump, cited Japanese internment camps during World War II as "precedent" for the database.

Speaking at the Women's March on Washington, women's rights campaigner Gloria Steinem said: "If you try to make Muslims register, we will all register as Muslim. So don't try to divide us."

Mayim Bialik, the trained neuroscientist and actress, earlier this week wrote on Twitter: "I stand ready to register as a Muslim in #solidarity if it comes to that", echoing a vow made by anti-Defamation League chief Mr Greenblatt last year.

Ms Albright was the first woman to be Secretary of State, serving alongside President Bill Clinton. She was born in Prague, fled the Hitler regime as a child, and speaks six languages.