An obscure court set up 30 years ago to expel immigrants accused of terrorism from the country heard its first case on Thursday, as the Justice Department asked a federal judge to deport an Afghan woman who prosecutors say supports the Islamic State.

The request took place at a nearly hourlong hearing in Washington before what is known as the Alien Terrorist Removal Court. During the hearing, prosecutors presented their initial claims that the woman, Nazira Haji Zada, should be removed from the United States even though she is a lawful permanent resident. The court was created by Congress in 1996 to handle deportation proceedings that largely rest on classified information.

The government contends that Ms. Zada, 47, is connected to a foiled terrorist plot inspired by ISIS to commit a mass shooting on Election Day in 2024. Last year, both her son, Abdullah Haji Zada, and her son-in-law, Nasir Ahmad Tawhedi, pleaded guilty to charges connected to the plot and admitted they had tried to buy two AK-47-style rifles and 500 rounds of ammunition to carry it out.

“The allegations in this case show the matriarch of an ISIS-sympathizing family aiding in a plot to launch a mass casualty attack on American voters on Election Day,” the acting attorney general, Todd Blanche, said in a statement before the hearing began. Ms. Zada, who appeared before a packed courtroom in a creamy white head scarf and flowing blue pants, was arrested on Tuesday at her home in Fort Worth, Texas, the court’s chief judge, Joan N. Ericksen, said.

The case against Ms. Zada is a test of a court where much of the evidence is presented in secret and defendants cannot challenge how it was collected. The Trump administration has used an expansive array of legal methods to carry out the president’s aggressive deportation agenda — many of them challenged in court. Now, it is seeking to use the sweeping powers of the terrorist removal court.

Ms. Zada has not been publicly charged with any crimes of terrorism and has no criminal history, according to court papers. Still, in an unclassified summary of her case submitted to the court, prosecutors said she “supported” the Election Day conspiracy and “pledged loyalty to ISIS.”