As US immigration officials arrest hundreds in raids in major cities across the United States, anxiety is growing within Greater Boston, fueling reports of immigration enforcement and random arrests.

In a statement on Tuesday, Secretary of Homeland Security John Kelly said that Immigration Customs Enforcement (ICE) officers in the Los Angeles, Chicago, Atlanta, San Antonio and New York City areas last week arrested more than 680 individuals “who pose a threat to public safety, border security, or the integrity of our nation’s immigration system.” About 75 percent of those arrested were immigrants convicted of crimes.

Social media in Boston has been abuzz for the last few weeks with rumors of arrests and detentions. Some Twitter and Facebook users circulated photos purporting to show ICE officers arresting individuals on Geneva Avenue on Feb. 5. No verified reports of local raids comparable to those in other cities have been put forward, and rumors of individuals impersonating ICE officers on the MBTA and asking Hispanic riders for documentation were called unfounded by transit police.

Shawn Neudauer, a spokesman for ICE in Boston, said Tuesday that there are no active agency operations in New England, but “officers are out conducting targeted arrests” as usual.

Although the rumors of arrests in the city are “potentially true,” Neudauer said “ICE doesn’t conduct random arrests. We’re usually looking for somebody.” He did not have data available on the number of arrests or detentions ICE officials have made in the city of Boston.

ICE raids have been conducted in Boston in the past. A four-day operation in Nov. 2011 resulted in 53 arrests of immigrants with criminal convictions in 16 Massachusetts communities, including the Roxbury and Dorchester neighborhoods of Boston. And a four-day New England raid in Sept. 2014 led to the arrest of 81 individuals, among them convicted criminals, immigration fugitives, and other immigration violators.

Advocacy groups are sharing lists of suggested behavior for those stopped by immigration officials or asked to allow them into homes.

The American Civil Liberties Union tip sheet on those stopped by police, ICE, or the FBI advises individuals to remain calm and polite but notes that they have the right to remain silent and not consent to searches of their bodies beyond a pat-down or their vehicles unless police have reason to believe that they contain evidence of a crime.

If authorities come to a home, the ACLU advises residents to examine the warrant slipped underneath a door or held against a window and understand the distinctions between search, arrests, and removal/deportation warrants, the latter of which requires consent to enter a home.

Boston rarely turns over immigrants to immigration officials, a position codified as city policy after the City Council passed its version of the Trust Act in 2014, which pledges that Boston police will not hold immigrants for possible deportation. The exceptions are if ICE has a criminal warrant or if an individual has committed a serious crime that makes him or her an immediate danger to the general public.

Boston Police Commissioner William Evans said in an interview on WGBH with Jim Braude and Margery Eagan that his officers will maintain that standard even after President Trump signed an executive order to strip federal funding from sanctuary cities in late January.

“I’ve been with the police department for 37 years and I’ve never ever seen anyone targeted because of their immigration status. … If we pull someone over for a traffic violation and they are illegal, we could care less,’’ Evans said. “We are not the immigration police and I’ve made that clear. And our policy isn’t going to change given what’s going on now.”

In a report submitted to the City Council early this month, Evans said the police did not detain 15 undocumented immigrants who were subject to federal deportation in 2016. The year before, nine individuals who were immigrants with criminal records were turned over for deportation.