Hoda Muthana, 24, is in a Syrian refugee camp with her 18-month-old son after she fled what's left of the Islamic State's self-declared homeland.

Her lawyers say she regrets joining the organisation.

But the administration announced earlier this week that the US-born Muthana is not an American citizen because her father was a Yemeni diplomat at the time of her birth in New Jersey. That determination was initially made by the Obama administration after she joined IS.

"She does not have any legal basis, no valid US passport, no right to a passport, nor any visa to travel to the United States," Secretary of State Mike Pompeo said.

President Donald Trump said on Twitter he had directed Pompeo "not to allow Hoda Muthana back into the Country!"

A suit filed Thursday in Washington argues her father had ceased being a diplomat and she is a citizen entitled to return.

Hassan Shibly, a representative for the Muthana family and a staff member of the Council on American-Islamic Relations, tweeted Muthana was born in Hackensack, New Jersey, in October 1994, months after her father informed the US government he was no longer a diplomat.

Australian Associated Press