Federal immigration officials arrested more than 600 people across at least 11 states last week, detaining 40 people in the New York City area, law enforcement officials said on Sunday.

It remained unclear whether the actions by Immigration and Customs Enforcement agents were part of continuing operations to round up illegal immigrants with criminal convictions or a ramping-up of deportations by the Trump administration.

President Trump proclaimed on Twitter early Sunday morning: “The crackdown on illegal criminals is merely the keeping of my campaign promise. Gang members, drug dealers & others are being removed!”

But Gillian Christensen, acting press secretary for the Department of Homeland Security, said, “The focus of these targeted enforcement operations is consistent with the routine, targeted arrests carried out by ICE’s Fugitive Operations Teams on a daily basis.”

The contradiction heightened an already swelling fear among immigrants and their advocates.

The New York operation was planned one week ago and was part of a national action that was planned several weeks ago, Immigration and Customs Enforcement said.

“New York was late to the game,” said an agency official who spoke on the condition of anonymity because details about who had been detained were still being learned. The official said the arrests had not been impromptu and had been planned around individuals’ routines, adding that a fuller account would be available on Monday.

“All these people are in violation of some sort of immigration law,” the official said, adding that some of their convictions included rape and aggravated assault. “We’re not going out to Walmart to check papers — we know who we are going out to seek.”

At least in the New York area (including Long Island), fewer people were arrested than during an Obama administration enforcement sweep in August, when 58 people were arrested.

The Obama administration was especially active in deporting unauthorized immigrants, most notably in 2012, when 409,849 people were deported. In 2015, Immigration and Customs Enforcement announced the arrests of more than 2,000 people nationwide in one week, targeting criminals. And the Obama administration was still sweeping up low-priority immigrants last summer.

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.

“Absolutely not!” Ms. Christensen, the Homeland Security spokeswoman, said. “That is completely false and an example of the many kinds of irresponsible, baseless fear-mongering we’ve been seeing.”

Through a statement from his spokeswoman Rosemary Boeglin, Mayor Bill de Blasio tried to reassure New York City’s immigrants on Sunday. “New Yorkers should rest assured that city officials, including the N.Y.P.D., will never ask about your immigration status, and the N.Y.P.D. will never become immigration enforcement agents,” Ms. Boeglin said.

New York is a so-called sanctuary city, which means that it generally does not comply with requests by immigration authorities to hold illegal immigrants who have committed low-level crimes. Mr. Trump has threatened to withhold federal funding for such cities.

On Long Island, activity by Immigration and Customs Enforcement agents had not yet reached the level of the large-scale enforcement seen under the George W. Bush administration. In one week in 2007, 170 people were arrested in Nassau and Suffolk Counties, said Pat Young, the program director of the Central American Refugee Center on Long Island.

“At least so far, it’s important to know that in the New York area, we haven’t had checkpoints; we haven’t had sweeps,” he said. “They are taking place at homes.”

Mr. Young said the “contradictory messages” of the president’s Twitter post and the immigration agency’s statements had stirred additional anxiety in the immigrant community.