Many of the arrests took place at immigrants’ homes, as teams of agents spread out in the early hours of the morning to catch people before they left for work, a common tactic designed to avoid a public scene. But agents also have been moving more aggressively, taking into custody people who arrived for routine check-ins, and even apprehending people arriving at courthouses on nonimmigration matters.

The rapid increase in arrests was primarily the result of one of Mr. Trump’s first significant immigration moves, rescinding rules laid down by former President Barack Obama that prioritized the arrest of the most serious criminals and largely left other undocumented immigrants alone. More than half of the increase in arrests were of immigrants who had committed no crime other than being in the country without permission.

Mr. Obama’s policy was rooted in both humanitarian and budgetary reasons, but to Mr. Trump and his supporters, and many ICE agents, it represented a failure to enforce the law and a de facto amnesty for millions of people in the United States illegally.

Supporters of Mr. Trump’s immigration policies welcomed the news. “I feel that’s one step in the right direction, I definitely feel that way,” said J. D. Ma, a lawyer in Clarksville, Md., who voted for Hillary Clinton but agreed with the president on immigration. “The reality is that if you don’t do that, that’s going to encourage wave after wave and disrupt the order of the society.”