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 ICE has reviewed "several hundred cases" of immigrants being held in jails around the country and released them in the last week. They have been "placed on an appropriate, more cost-effective form of supervised release," she said.

Christensen said the agency's "priority for detention remains on serious criminal offenders and other individuals who pose a significant threat to public safety." She did not say how released immigrants were selected or what jails they were released from.

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. On average last week, there were 30,773 people being held in ICE jails.

"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.

Republicans lawmakers decried the releases Tuesday.

"It's abhorrent that President (Barack) Obama is releasing criminals into our communities to promote his political agenda on sequestration," House Judiciary Committee Chairman Bob Goodlatte. "By releasing criminal immigrants onto the streets, the Administration is needlessly endangering American lives. It also undermines our efforts to come together with the Administration and reform our nation's immigration laws."

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.