"We continue to strongly advise all USA citizens not to travel to Syria", he added.
In Muthana's case, both sides are at odds over whether the woman, who was born in Hackensack, New Jersey, was ever a USA citizen in the first place.
Secretary of State Mike Pompeo said in a statement released on Wednesday that Muthana's request will not be accommodated. "She is not a USA citizen, nor is she entitled to USA citizenship", Pompeo told NBC television's "Today" show.
Muthana's status had been considered by lawyers from the departments of State and Justice since her case arose, according to one US official who was not authorized to discuss the matter publicly and spoke on condition of anonymity.
"Ms. Hoda Muthana is not a U.S. citizen and will not be admitted into the United States".
Muthana claimed that the reason she left her family to go to ISIS was to live a more "Americanized life".
With her 18-month-old son balanced on her lap, she said she had given up the extremist "ideology" that convinced her to leave her family and that she wanted to be welcomed home by the American people.
Mr Shibly, a lawyer with the Florida branch of the Council on American-Islamic Relations, said: "She's an American". A lawyer for the family says 19-year-old Shamima Begum's citizenship is being revoked - an action that could render her stateless.
The lawyer for the family of the Alabama woman turned ISIS wife in Syria tells "America's Newsroom" that Hoda Muthana is a USA citizen who wants to face the American legal system and pay her debt to society.
Meanwhile, other countries are facing similar decisions about what to do with Muslims who joined the Islamic State in Iraq and Syria.
When interviewed by ABC, she expressed remorse and regret about her social media posts inciting violence in the name of Islam and ISIS. "She's not entitled to US citizenship". Now, she says she "deeply regrets" supporting the terrorists and inciting hatred on social media.
Muthana and her son are now in a refugee camp in Syria, along with others who fled the remnants of the Islamic State.
He also released a 2004 document from the U.S. Mission to the United Nations certifying that Muthana's father was serving as a diplomat until September 1, 1994, one month before Muthana was born.
Just this weekend, Trump took to Twitter to chastise European allies that have not taken back hundreds of Islamic State prisoners caught in Syria, where Trump plans to withdraw USA troops.
The bloodshed was more severe in person, she said, than she could have ever imagined and becoming a mother made her more sensitive to it. But US officials seem to be hinging their argument against allowing her back in on an exception in the law.
"During my years in Syria I would see and experience a way of life and the awful effects of war which changed me", she wrote.
Hoda Muthana, 24, left Alabama for Syria where she married three Isil jihadists and had a child.