When Brad Lander, the New York City comptroller, was arrested on Tuesday by federal agents at an immigration courthouse in Manhattan, Mr. Lander said he had simply been trying to escort an immigrant whom agents wanted to detain.

His arrest underscored a trend that has emerged in New York City’s immigration courts: A growing number of volunteers and activists have begun showing up to escort immigrants out of courthouses amid President Trump’s month-old campaign to arrest people showing up for routine hearings.

During the past few weeks, a loose network of immigration activists and advocates has sprung up in the city’s three main immigration courts. Their goal, they say, is to help immigrants who show up without lawyers to navigate a labyrinthine and daunting system, and to accompany migrants past federal officers, who are often masked and not wearing uniforms.

Before, volunteers might have accompanied immigrants to hearings, but only in recent weeks have they had to consider what happens when they leave “because ICE wasn’t waiting on the other side of the door before,” said Camille J. Mackler, the founder and executive director of Immigrant ARC, a collaborative of immigration legal services providers. “We really are just there to bear witness in a nonviolent way.”

Mr. Lander, who is running for mayor, maintained that is what he was trying to do on Tuesday when federal officers approached an immigrant named Edgardo to arrest him. Video shows Mr. Lander appearing to hold on to Edgardo and refusing to let go as officers were trying to arrest the man over Mr. Lander’s protestations.

The Department of Homeland Security saw it differently. The agency accused Mr. Lander of assaulting and obstructing federal officers as they were performing their duties, all to boost his mayoral campaign.