(CNN) A 31-year-old Mexican national is the first detainee in Immigration and Customs Enforcement custody to test positive for the novel coronavirus, the agency announced Tuesday.

The detainee, who has been held at the Bergen County Jail in Hackensack, New Jersey, has been quarantined and is receiving care, ICE said, adding that the agency "is suspending intake at the facility until further information is available."

"Consistent with CDC guidelines, those who have come in contact with the individual have been cohorted and are being monitored for symptoms," ICE said.

ICE's statement Tuesday did not specify how long the detainee had been in custody or provide any details about how the detainee contracted coronavirus. A corrections officer working at the facility tested positive for the virus last week. At the time, the sheriff's office said in a statement that no ICE detainees had been exposed.

Calls to release detainees mount

Some advocates are asking for the agency to release detainees with underlying medical conditions and are filing federal lawsuits to force the government's hand. Others are pushing even further, saying all detainees should be let out.

On Tuesday, organizations that have been pushing for detainees to be released pointed to the first coronavirus case in ICE detention as a sign that time is running out. New York public defenders said in a statement that they are "deeply concerned" for their clients in ICE custody and noted that detainees in several facilities have been conducting hunger strikes to protest conditions.

"ICE's continued inaction made today's confirmed COVID-19 case in ICE detention a virtual inevitability and further highlights the urgent need to release all individuals in ICE custody immediately," the statement said. "For weeks, we have received many disturbing reports from our detained clients about the unsanitary conditions that are putting their lives at risk."

Advocates' campaigns for immigration detainees to be released have drawn sharp criticism from organizations that support the government's crackdown on illegal immigration. Some have a rgued the US should instead increase the pace of deportations to lower the number of people detained.

Doctors weigh in

On Friday two doctors who are medical experts for the Department of Homeland Security sent a letter to Congress arguing that the department should consider releasing all immigrant detainees who don't pose a risk to public safety, before it's too late.

The doctors, contracted experts for the Department of Homeland Security's Office for Civil Rights and Civil Liberties, wrote they were "gravely concerned" about the threat the novel coronavirus poses.

Asked for a response to the concerns raised in the doctors' letter, an ICE spokeswoman pointed to the agency's website, where ICE is posting coronavirus updates . The site describes the health and safety of detainees as a top priority and details how the agency plans to mitigate the spread of the virus.

"ICE continues to incorporate CDC's COVID-19 guidance, which is built upon the already established infectious disease monitoring and management protocols currently in use by the agency," the site says. "In addition, ICE is actively working with state and local health partners to determine if any detainee requires additional testing or monitoring to combat the spread of the virus."

ACLU: Detainees are 'sitting ducks'

As part of its efforts to stop coronavirus from spreading, ICE recently announced it was temporarily suspending social visitation at its facilities "as a precautionary measure" -- meaning family members, friends and advocates who used to be able to visit detained loved ones in person can't anymore, at least for now.

The American Civil Liberties Union, which has filed several recent lawsuits pushing for ICE detainees to be released, said in a statement Tuesday that the first confirmed case was "what public health experts have assured us would happen."

"People in detention centers are sitting ducks for the spread of this virus," said Andrea Flores, the deputy director of policy for the organization's equality division. "The same experts have also predicted that once outbreaks in detention centers begin, they will spread rapidly. The suffering and death that will occur is unnecessary and preventable."