Based on that finding, at least 13,000 American children have seen one or both parents deported in the past two years after round-ups in factories and neighborhoods. The figures are expected to grow. Over all, about 3.1 million American children have at least one parent who is an illegal immigrant, according to a widely accepted estimate by the Pew Hispanic Center in Washington.

Under the 14th Amendment, any child born in the United States is a citizen and cannot be deported. But with very rare exceptions, immigration law does not allow United States citizen children to confer legal status on parents who are illegal immigrants, until the children are 21 years old. While the federal government does not keep statistics on the children of deportees, immigration lawyers said that most immigrants who are deported take their children with them, even if the children are American citizens.

“Children have no rights to keep family members here because they are citizens,” said Jacqueline Bhabha, a lecturer at Harvard Law School who specializes in citizenship law. When parents face deportation, she said, the law “penalizes United States citizen children by forcing them to choose between their family and their country.”

Ms. Umanzor, 26, was arrested in her home on Maple Street in Conneaut, Ohio, on Oct. 26 and was released 11 days later on orders of Julie L. Myers, the head of the immigration agency. While in detention, Ms. Umanzor did not see her daughter Brittney, who had been fed only breast milk before her mother’s arrest. Ms. Umanzor remains under house arrest with Brittney and her two other children in Conneaut, 70 miles east of Cleveland, under an order for deportation. Her lawyer, David W. Leopold, has asked that her deportation be delayed on humanitarian grounds.

Ms. Umanzor had been at home with two of her three children, both American citizens, when the immigration agents arrived, along with a county police officer carrying a criminal warrant for a brother-in-law of Ms. Umanzor who also lived in the house.

As the agents searched, Ms. Umanzor breast-fed her jittery baby, she recalled in an interview after her release.

Image Saída Umanzor, an illegal immigrant who was detained last month and separated from her 9-month-old, Brittney Bejarano. Credit... Scott Shaw for The New York Times

The baby was born in January in Oregon, where Ms. Umanzor’s husband, also Honduran and an illegal immigrant, was working in a saw mill.