(CNN) President Donald Trump said Wednesday that he directed Secretary of State Mike Pompeo not to allow Hoda Muthana, an Alabama woman who left in November 2014 to join ISIS , to return to the United States -- despite her recent public plea to come back and stand trial in America.

"I have instructed Secretary of State Mike Pompeo, and he fully agrees, not to allow Hoda Muthana back into the Country!," Trump tweeted.

Hours earlier, Pompeo declared that Muthana, who is detained in a Kurdish refugee camp, is not an American citizen.

"Ms. Hoda Muthana is not a U.S. citizen and will not be admitted into the United States. She does not have any legal basis, no valid U.S. passport, no right to a passport, nor any visa to travel to the United States," Pompeo said in a statement.

Muthana, now 24, was a college student when she traveled to Syria over four years ago to join ISIS -- eventually marrying three fighters and calling for the killing of Americans on Twitter. In a series of interviews this week from a sprawling camp in northern Syria with her infant son, she expressed deep remorse.

"When I left to Syria I was a naive, angry, and arrogant young woman," she said in a handwritten statement provided to CNN by a representative. "To say that I regret my past words, any pain that I caused my family and any concerns I would cause my country would be hard for me to really express properly."

Hassan Shibly, a family representative for Muthana, denied that she was not a citizen, and called the move by the Trump administration to claim otherwise "very dangerous."

According to Shibly, Muthana was born in New Jersey in 1994. Her father, who had been in the US as a Yemeni diplomat, stepped down from his diplomatic role months before Muthana's birth, Shibly added.

‪"The Trump administration continues its attempts to wrongfully strip citizens of their citizenship," Shibly said in statement.‬

"‪Hoda Muthana had a valid US passport and is a citizen. She was born in Hackensack, NJ in October 1994, months after her father stopped being diplomat‬," he added before later tweeting a picture of what he claimed is Muthana's birth certificate, that appeared to confirm her place and date of birth.

However, a State Department spokesperson said Wednesday evening that Muthana "was not born a U.S. citizen and she has never been a U.S. citizen."

"Ms. Muthana's citizenship has not been revoked because she was never a US citizen," they added.

Under US law Muthana would be a US citizen by nature of her birth in the country, though the State Department could argue that her claim to citizenship is flawed because of the immigration status of her parents at the time of her birth.

Muthana's family plans to file a lawsuit challenging the government's assertion that she is not a citizen this week, according to Charles Swift, who represents Muthana's father.

Stephen Yale-Loehr, an immigration lawyer and Cornell University professor, said that the situation is "not clear-cut."

"It would depend on the facts, if the State Department argues that her father's diplomatic status was still in effect. The family argues it expired. So ultimately, it may be up to a court to sort this out," he told CNN.

Yale-Loehr said that if Muthana had a US passport, "that means that somebody at that point made the determination that she was a US citizen." However, he noted that many of the facts are still unknown.

The State Department spokesperson said, "There are many reasons that an individual previously issued a passport may subsequently be found ineligible for that passport."

"If it is determined that the bearer was not entitled to the issued passport, the passport may be revoked and/or a renewal application denied," they said.

Asked about Muthana's case on Tuesday, State Department deputy spokesperson Robert Palladino noted that "the situation of American citizens or possible American citizens in Syria is by definition extremely complicated and we're looking into these cases to better understand the details."

Palladino would not speak to the specific case, but said that in cases involving "American citizens or potential American citizens or alleged American citizens," US policy "would be to repatriate them, and it's what we call on all countries to do who have (foreign terrorist) fighters in Syria too."

Muthana grew up in Hoover, Alabama, in a Yemeni household that she has called ultra-strict. In interviews with The Guardian The New York Times and ABC News from the Al Hawl refugee camp this week, she described how she used money from her parents meant for tuition at the University of Alabama at Birmingham to pay for a flight to Istanbul in late 2014.

After being smuggled into ISIS-controlled territory, she tweeted a photo of an American passport, with the caption "bonfire soon, no need for these anymore."

In the caliphate, she become a noted ISIS propagandist online, her presence on Twitter growing extreme and violent.

"Soooo many Aussies and Brits here, but where are the Americans, wake up u cowards," she posted in January 2015.

"Go on drive-bys and spill all of their blood, or rent a big truck and drive all over them," she wrote that March.

In her written statement, she said that years of bloodshed and war, and the birth of her son, changed her.

"In my quiet moments, in between bombings, starvation, cold, and fear, I would look at my beautiful little boy and know that I didn't belong here and neither did he," she wrote.

Last month, as Kurdish forces backed by US-led coalition aircraft beat ISIS back to territory only kilometers wide, she decided to attempt an escape.

On January 10, she told the Times, she surrendered to American troops in the Syrian desert.

The US's refusal to repatriate Muthana comes just days after Trump criticized European allies for not taking back their own captured citizens.

More than 800 foreign fighters from more than 40 countries are currently being held by the US-backed Syrian Democratic Forces, according to the Pentagon. Women who married the ISIS fighters, known as ISIS brides, and their children are also being held in detention by the Kurds.

Many countries are reluctant to repatriate them because of the difficulty of prosecuting suspected ISIS members based on evidence collected on the battlefield, causing frustration among US national security officials.

"The alternative is not a good one in that we will be forced to release them," Trump tweeted Sunday. "The U.S. does not want to watch as these ISIS fighters permeate Europe, which is where they are expected to go."

The number of Americans who joined ISIS on the battlefield, like Muthana, are small, compared to countries like France and the UK, from where several hundred foreign fighters traveled, according to international reports. The US has, however, prosecuted a number of their foreign fighters.

Some 59 Americans are believed to have joined the Islamic State, and 13, including a Texas man just last month, have faced terror-related charges after being returned to the US, according to research from the George Washington University Program on Extremism. Many more are believed to have died on the battlefield.