Mr. Bible said that one of the buildings was used for executive administration and that his agency occupied the top two floors. The second building housed a contractor that works for ICE, he said.

Amid continued anger over the crisis at the border, calls to abolish or defund ICE last year became a rallying cry among some Democrats, including Representative Alexandria Ocasio-Cortez, who campaigned on eliminating the agency.

When asked about the national immigration debate, as well as calls for the elimination of his job, Mr. Bible said the discourse was “reckless.”

“My officers are out there every day doing things to make our community safer,” Mr. Bible said.

While the extent of the damage from Tuesday’s shootings was not immediately clear, Kenneth T. Cuccinelli II, the acting director for the United States Citizenship and Immigration Services, shared a photo of a bullet hole on Twitter later in the day. (Mr. Cuccinelli was also facing backlash for remarks in which he adapted the poem on the Statue of Liberty to a more Trumpian view of immigration — “Well, of course, that poem was referring back to people coming from Europe,” he said on CNN on Tuesday.)

“@USCIS stands with @ICE as they work to enforce our laws and keep Americans safe,” he tweeted.