A hearing on Tuesday at immigration court in Van Nuys, Calif., was supposed to be routine for a young family from Colombia, the first step in what they hoped would be a successful bid for asylum.

To their surprise, the judge informed the father, Andres Roballo, that the government wished to dismiss his deportation case. Taken aback, Mr. Roballo hesitated, then responded: “As long as I stay with my family.”

Moments later, as they exited the courtroom into a waiting area, Mr. Roballo was encircled by plainclothes federal agents who ushered him into a side room. Other agents guided his shaken wife, Luisa Bernal, and their toddler toward the elevator.

Outside the courthouse, Ms. Bernal collapsed on a bench. “They have him, they have him,” she wailed. “We didn’t understand this would happen.”

Mr. Roballo’s arrest was part of an aggressive new initiative by Immigration and Customs Enforcement to detain migrants at immigration courts, the latest escalation by the Trump administration in its all-out effort to ramp up deportations.

Agents have begun arresting migrants immediately after their hearings if they have been ordered deported or their cases have been dismissed, a move that enables their swift removal, according to immigration lawyers and internal documents obtained by The New York Times.