WASHINGTON — A week before mandatory budget cuts go into effect across the government, the Department of Homeland Security has started releasing illegal immigrants being held in immigration jails across the country, Immigration and Customs Enforcement said Tuesday.

Gillian Christensen, an ICE spokeswoman, said immigrants being held in jails around the country have been released and “placed on an appropriate, more cost-effective form of supervised release.” Christensen did not say how many people were being released or how they were selected.

Tuesday’s announcement of jail releases is the first tangible impact of the looming budget cuts for DHS.

The Obama administration has been issuing dire warnings about the impact of the sequestration and DHS Secretary Janet Napolitano told reporters at the White House Monday that across-the-board cuts would impact the department’s core operations, including border security and airport screening operations.

She also warned that DHS might not be able to afford to keep the 34,000 immigration jail beds mandated by Congress.

“I don’t think we can maintain the same level of security at all places around the country with sequester as without sequester,” said Napolitano, adding that the impact would be “‘like a rolling ball. It will keep growing.”

According to the National Immigration Forum, it costs the government about $164 a day to keep an illegal immigrant facing deportation jailed. In a report on immigration detention costs last year the advocacy group said costs for supervised release can range from about 30 cents to $14 a day.

The administration asked for about $1.96 billion for immigration jail operations in the last budget. It amounts to about $5.4 million a day, according to the National Immigration Forum’s report.

Christensen said Tuesday that released immigrants will still face deportation proceedings.