Less than a week after a failed attempt to petition for the release of a group of inmates in New York City jails, New York's Legal Aid Society filed suit Tuesday on behalf of 32 more inmates vulnerable to the coronavirus.

The new filing emphasized the spike in COVID-19 cases at Rikers Island over the weekend and provided more details about each inmate, including, in some cases, the names of jail doctors who have recommended their release.

The new filing is the latest in a series of efforts by advocates and even some elected officials to free medically vulnerable inmates and those charged with some nonviolent crimes from jails and prisons around the United States.

Calls for widespread release in New York grew more pointed in recent days as other states, including New Jersey, announced the release of large groups of inmates.

ACLU-New Jersey, which fought for the New Jersey Supreme Court order releasing low-risk inmates, estimated that it would affect as many as 1,000 inmates.

New York City Mayor Bill de Blasio said in a Tuesday afternoon press conference that he didn't have the authority to release most city jail inmates by himself, but he said about 300 inmates serving short sentences will be immediately released and several hundred more inmates were under review.

In the suit filed Tuesday by Legal Aid, Corey Stoughton, attorney in charge of the Special Litigation Unit of the Legal Aid Society's Criminal Defense Practice, said Legal Aid lawyers are still hearing from some clients in jail who lack access to soap or hand sanitizer.

"There have been shortages of basic cleaning supplies to disinfect housing areas in New York City jails, including housing areas where people with respiratory illnesses are confined," she wrote. On Monday, one lawyer heard from a client who said his dorm had not been cleaned even though several people had been removed from the area after testing positive for the coronavirus.

On Friday, Stoughton filed a petition on behalf of 116 inmates and argued it in court that afternoon. She explained that the petition was rejected because the judge didn't agree that Legal Aid had proved that continuing to hold the inmates constituted deliberate indifference to the risk of serious medical harm under the Fourteenth Amendment.

A spokesman for the New York City Law Department said his office is reviewing Tuesday's filing.