Five inmates at the Metropolitan Correctional Center on Tuesday accused the troubled Manhattan jail and its warden of "ineptitude and indifference," as federal prison officials in New York continued to report minimal levels of testing in response to the COVID-19 pandemic.

In a proposed class action lawsuit, filed in Manhattan federal court by a Covington & Burling partner, said the coronavirus was spreading "unmonitored and undetected throughout the jail," due in large part to overcrowding and unsanitary conditions.

Officials, the suit alleged, had also failed to remove symptomatic inmates from larger dormitories, where more than two dozen men bunk in close quarters and share just a single toilet and one or two sinks. Inmates suspected of being infected with the disease have only received, "at best, only cursory medical attention," and testing and tracing were nearly nonexistent, according to the filing.

"Judicial intervention is required to compel the MCC to improve conditions of incarceration and take other steps to comply with the requirements of the U.S. Constitution and lessen the risk of serious illness or the death of individuals in its care," Covington & Burling partner Arlo Devlin-Brown wrote on behalf of the plaintiffs.

The lawsuit was filed on behalf of five inmates, who MCC had identified as particularly vulnerable to the disease based on criteria published by the Centers for Disease Control and Prevention. Some of the plaintiffs were suffering from COVID-19 or feared they might contract the virus due to their proximity to other inmates. According to the filing, none had been tested for the disease.

The 29-page complaint, which alleged violations of the Fifth and Eighth Amendments to the U.S. Constitution, mirrored a similar lawsuit filed in Eastern District of New York on behalf of inmates at Brooklyn's Metropolitan Detention Center, and it asked for a court order mandating MCC and its warden, Marti Licon-Vitale, to implement appropriate tracking, testing and social-distancing measures.

The federal Bureau of Prisons did not immediately respond Tuesday to a request for comment.

As of Tuesday, a total of 21 inmates have been tested for coronavirus at MCC and MDC combined, a small increase compared to 19 last week. Eleven of those tests have come back positive, according to the report. Staff cases of coronavirus continue to increase at both facilities, from 59 on Thursday to 69 Tuesday.

The MCC and MDC wardens are required to report on their coronavirus testing twice weekly under an April 2 order from U.S. District Chief Judge Roslynn Mauskopf, who also ordered the wardens to report on "all efforts undertaken to mitigate the spread of COVID-19."

In each report so far, the wardens have described their enactment of the Bureau of Prisons' national action plan to promote social distancing, which includes limiting the time inmates spend outside their cells.

"The national action plan will not, however, affect the provision of legal phone calls," they repeated in each report. "Inmates will still be taken out of their cells for legal phone calls."

Lawyers representing inmates at the MDC in an ongoing suit against the Bureau of Prisons have repeatedly said that's not the case, telling U.S. District Judge Margo Brodie of the Eastern District of New York that their clients' requests for calls have been ignored and the calls that do happen tend to be short.

Sean Hecker of Kaplan Hecker & Fink, who is representing MDC inmates alongside the Federal Defenders of New York, filed a letter Tuesday telling Brodie that inmates in medical isolation are still struggling to reach their attorneys. Four legal calls were scheduled Monday for inmates in isolation, but only one call took place, Hecker wrote.

"We wanted to inform the Court of this issue immediately, because whatever the reason, we respectfully request that the BOP be instructed that such calls are mandatory, and if there is a particular reason why a call with an inmate in medical isolation cannot be placed on a particular day, the BOP should immediately inform counsel for the inmate of that, and reschedule the call, not simply choose not to place the call," Hecker wrote.

Physical visits between attorneys and inmates are suspended due to coronavirus restrictions, and Brodie has noted that both the MDC and MCC still need to make progress in ensuring that inmates have access to their lawyers.

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