NORTH BRUNSWICK -- For the second time in two months, a pair of undocumented immigrants ordered held for deportation by the U.S. Immigration and Customs Enforcement were released from the Middlesex County jail without notification, ICE officials said.

A Mexican citizen and an Indian citizen were arrested by ICE's Enforcement and Removal Operations officers about two weeks after the county jail released them, ICE said in a news release Monday. The two men remain in custody awaiting deportation, the agency said.

John Tsoukaris, director of the agency's Enforcement and Removal Operations field office in Newark, said county jails that fail to work with ICE put their communities at risk.

"As a nation, we must protect the integrity of our immigration system and the removal of illegal aliens, especially those with a criminal history. This is one of ICE's top priorities," Tsoukaris said in a statement. "ICE shares the county's ultimate objective to protect public safety and national security while simultaneously preserving the critical community police bond."

Middlesex County officials could not immediately be reached for comment Monday evening.

ICE lodged an immigration detainer May 18 on Aurelio Hernandez Cortez, the Mexican citizen, with the county jail. The same day, the jail released him from custody without notifying them, ICE said in its statement.

Officers arrested Hernandez Cortez on June 8 outside his residence in Perth Amboy, the agency said. He faces criminal charges in Middlesex County, which ICE did not disclose.

On May 22, ICE lodged an immigration detainer on Maulik Gajjar, an Indian citizen, with the county jail. On the same day, the facility released him without notifying ICE, the agency said.

Officers arrested Gajjar on June 7 outside his residence in Iselin. He faces state criminal charges, which ICE did not disclose.

The arrests were made about a week after the county's Board of Chosen Freeholders adopted an official policy limiting the county law enforcement's cooperation with the federal agency.

Under the new policy, Middlesex County authorities will refuse to honor ICE's two-day hold orders unless the person has been convicted of a first- or second-degree serious offense, including murder, drug distribution and carjacking and sex assault.

The policy prohibits the sheriff's office from assisting ICE with anyone not already in jail. Sheriffs will also only release inmates or detain someone if immigration officers have a warrant of removal or deportation from a federal judge, according to the policy.

ICE criticized the county the same day it adopted the new policy for releasing a Honduran national and Mexican citizen without the telling the agency.

The federal agency filed an immigration detainer for Elder Antonio Quintero Rodriguez in April 2016 for his felony conviction of neglect of a child, ICE said. He was released from the county jail May 19, officials said.

In late April, a detainer was issued for Rolando Herrera Saavedra, authorities said. A week later, Saavedra was released from jail, officials said. He faces state criminal charges, which ICE did not disclosed.

The two men were arrested by ICE officials in late May, the agency said.

Craig McCarthy contributed to this report.

Luke Nozicka may be reached at lnozicka@njadvancemedia.com. Follow him on Twitter @lukenozicka. Find NJ.com on Facebook.