A prisoner in the Middleton House of Correction become Massachusetts' first county jail inmate to die of COVID-related causes, heightening concerns among advocates that not enough is being done to reduce incarcerated populations, test inmates or prevent the spread in the state penal system.

Essex County Sheriff Kevin Coppinger said Thursday that the 41-year-old prisoner died Wednesday, was one of 60 in his facilities to have tested positive for the virus. The prisoner — whose name was not released — had other health issues and had been incarcerated in the jail since Feb. 18, county officials said.

“My heartfelt thoughts and prayers are with this man’s family,” Coppinger said in a news release. “This pandemic continues to wreak havoc bringing tremendous heartache to so many families in all walks of life.”

The county jail death adds to seven state prisoners who have died of COVID-related complications since early April, according to the state Department of Correction.

Meanwhile the number of inmates testing positive continues to rise in Massachusetts. So far, 376 inmates have tested positive in 13 county jails and 16 state prison facilities, according to the most recent data collected by the American Civil Liberties Union. This is up from 18 on April 5, data shows.

A state Superior Court judge has been holding remote hearings this week related to a lawsuit filed by the nonprofit Boston-based Prisoners’ Legal Services. The group claims the government is failing to adequately reduce incarcerated populations and stop the spread of the virus, violating the constitutional rights of the incarcerated.

Judge Robert Ullman has been tasked with interviewing witnesses — including Department of Correction Commissioner Carol A. Mici on Wednesday — to present information to the state Supreme Judicial Court. The state’s top court is expected to hold a hearing in early May.

Elizabeth Matos, executive director of the prisoners’ advocacy group, says until government officials reduce inmate numbers the state will see increased infections behind bars.

“The reality is that many of these jails are overcrowded, they rely on dorm settings, and as long as we have this many people in jails and prisons we will continue to see the virus spread,’’ Matos said.

On Wednesday, Mici testified that her agency is doing everything possible to prevent infection among its 7,500 prisoners. The prisons have been on lockdown since early April — a situation Mici described as “sheltering in place” — and inmates have recently been provided masks, she said.

But Mici acknowledged challenges. She said nearly 60 percent of prisoners can’t properly social distance because they live in shared cells or dorm rooms. Some inmates who have tested positive are in the same units with those who haven’t, she said, sharing the same showers. And some staff and inmates have been resistant to wearing masks.

“I already have had inmates refuse and flush them down the toilet,” she told the judge. “That’s what we are up against.”

Advocates also are concerned that jails and prisons aren’t doing enough testing to know the extent of the problem behind bars. Some county sheriffs have not tested any prisoners at all while the number of COVID-positive inmates in the state prison system began to surge after the DOC began to test prisoners within entire facilities.

“We are really alarmed because in the places where people are being tested many seem to have it,’’ said Matthew Segal, legal director for the state ACLU. “We need far more testing.”

Mostly advocates hope to see the governor and state Parole Board do more to release prisoners. In early April the state Supreme Judicial Court ruled that inmates who are awaiting trial and not charged with certain violent, serious offenses can seek release with a presumption that they we will be let go unless they are considered to be an “unreasonable danger” or a flight risk.

The court also urged the state Department of Correction and the Parole Board to expedite parole hearings and increase the release of prisoners already approved for parole and those nearing the end of their sentences.

Since then, there have been 654 prisoners released pursuant to the ruling, according to the ACLU data tracker. Only 15 of those were released from the state prison system.

Katy Naples-Mitchell a legal fellow at the Charles Hamilton Houston Institute for Race & Justice at Harvard Law School, says she’s watching the number of cases rise with concern.

“We are watching a pretty rapidly moving disaster,’’ she said. “It’s impossible to contain a virus like this inside.”