A spokeswoman for Immigration and Customs Enforcement, or ICE, an arm of the Department of Homeland Security, said the detainees selected for release were “noncriminals and other low-risk offenders who do not have serious criminal histories.”

Officials said the releases, which began last week and continued on Tuesday, were a response to the possibility of automatic governmentwide budget cuts, known as sequestration, which are scheduled to take effect on Friday.

“As fiscal uncertainty remains over the continuing resolution and possible sequestration, ICE has reviewed its detained population to ensure detention levels stay within ICE’s current budget,” the agency’s spokeswoman, Gillian M. Christensen, said in a statement. The agency’s budget for custody operations in the current fiscal year is $2.05 billion, officials said, and as of Saturday, ICE was holding 30,773 people in its detention system.

Immigration officials said Tuesday that they had no plans to release substantially more detainees this week, though they warned that more releases were still possible depending on the outcome of budget negotiations.

They refused to specify exactly how many detainees were released, or where the releases took place. But immigrants’ advocates around the country have reported that detainees were freed in several places, including Hudson County, N.J.; Polk County, Tex.; Broward County, Fla.; New Orleans; and from centers in Alabama, Arizona, Georgia and New York.