The case has sparked outrage among pro-immigration groups and Democrats, widening the gulf between the city and the federal government's determination to crack down on illegal immigration.

Pablo Villavicencio, 35, an undocumented migrant, was detained on June 1 at the Fort Hamilton Army Base in Brooklyn, after a military policeman was not satisfied with his New York identity card and a background check confirmed that he was not a legal resident.

Immigration and Customs Enforcement (ICE) were called and moved to deport him, until a federal judge temporarily blocked his deportation order. Villavicencio has remained in detention ever since.

His wife and daughters, aged two and four, are US citizens. His youngest daughter reportedly suffers from a heart defect.

"We're hopeful that Pablo and his family will be reunited shortly," Gregory Copeland from the Legal Aid Society told reporters Tuesday after a federal court hearing in Manhattan.

"This case is about a family that was torn apart and I think having that family reunited as soon as possible is what matters," he added.

At the hearing, Judge Paul Crotty questioned the rationale for deportation, given that Villavicencio has a pending application for permanent residency.

"Is there any concept of justice here or are we just doing it because we want to?" Crotty asked. "Where's the harm to the country?" he added. It was not clear when he would make a decision.

The US government wants the case transferred to New Jersey, where Villavicencio is being held. His lawyers want the case to remain in New York, where ICE is based, and his immediate release.

His wife, Sandra Chica, who was visibly emotional, and two daughters attended Tuesday's hearing. Villavicencio did not.

"Our lives have been completely upended," Chica said Monday. A small group of activists rallied outside court, calling for his release.

The Trump administration has sought to get tough on undocumented migrants, moving to deport even those without criminal records and with deep family ties to the United States.

Villavicencio entered the United States in 2008 and in 2010 ignored an order to leave. He married in 2013 and has no criminal record, always working and paying his taxes.