A former US Secretary of State and a Big Bang Theory actress have both vowed to register as Muslim if Donald Trump creates a database of Muslim Americans.

Politician Madeleine Albright and Mayim Bialik said they "stand ready" to register, in defiance of the new President.

"I was raised Catholic, became Episcopalian & found out later my family was Jewish," Ms Albright - the first woman to be named Secretary of State - tweeted on Wednesday.

"I stand ready to register as Muslim in #solidarity." The tweet gained tens of thousands of likes.

Her comments come as rumours continue to circulate about an executive order which would announce extreme vetting, a refugee ban and a ban on arrivals from seven countries, said to include Syria, Yemen and Iraq.

But there has been no mention of a register of American Muslims in recent months - something Mr Trump said he would "certainly implement" in an interview in 2015, but later distanced himself from.