Nevertheless, Steven Choi, the executive director of the New York Immigration Coalition, said last week’s action was worrisome because it seemed to be only the beginning.

“It really doesn’t matter if it’s business as usual from ICE’s perspective — at some point, we know that they will start to ramp up enforcement activity,” Mr. Choi said in an interview. He added that a Jan. 25 executive order from the president about ensuring public safety included the bolstering of the immigration force.

Mr. Trump’s executive order also vastly expanded the group of immigrants considered priorities for deportation, including those without criminal records.

When asked if the recent operations had incorporated the new priorities, a Homeland Security official, speaking on the condition of anonymity because operations were continuing, said, “The president has been clear in saying that D.H.S. should be focused on removing individuals who pose a threat to public safety, who have been charged with criminal offenses, who have committed multiple immigration violations or who have been deported and re-entered the country illegally.”

About 160 foreign nationals were recently arrested in six counties in the Los Angeles area, according to Immigration and Customs Enforcement officials. An additional 200 were arrested last week in Georgia, North Carolina and South Carolina. And about 200 were arrested across Illinois, Indiana, Kansas, Kentucky, Missouri and Wisconsin.

At least some of the rumors circulating on social media over the weekend proved to be false, including reports of raids in Jackson Heights, Queens, and in Huntington Station on Long Island. Similarly, immigration advocates in Kansas City, Mo., were on alert after hearing rumors that Immigration and Customs Enforcement agents planned to arrest people who were on their way to worship on Sunday.