After a spike in coronavirus infections this week at Santa Rita Jail, Alameda County Public Defender Brendon Woodscalled for the immediate release of more than 100 inmates who have less than six months left to serve.

Woods directed his request to District Attorney Nancy O’Malley’s office after sheriff’s officials announced on Thursday that COVID-19 cases jumped from 3 to 12 in two days. Officials at the Dublin jail have already released more than 600 inmates since the region’s shelter-in-place order took effect on March 17, and a new statewide order will eliminate bail to free dozens more awaiting trial.

“We need to take actions now,” Woods told The Chronicle. “I appreciate what’s been done, yes, but we can do more.”

Of the 115 inmates with less than six months to serve, about 59 are scheduled for release by the end of May, according to the public defender’s office. Modified sentences require sign-off from the district attorney’s office and courts overseeing the cases.

In a written statement, O’Malley said her office is working diligently with the public defender’s office to reduce the jail’s population.

“What we cannot do is jeopardize the safety of victims or the community,” she said. “We must take the necessary care and precaution to ensure the health of those incarcerated and the staff working at the jail without sacrificing the security of victims or well-being of the county. To do otherwise would be irresponsible.”

O’Malley also took a jab at Woods, saying it was “very disappointing that the Public Defender has chosen this time of crisis to grandstand and to make politically divisive and disingenuous statements.”

The first positive test at the jail was reported Saturday, followed by two on Tuesday, eight on Wednesday and one on Thursday.

Jails across the state in the last few weeks released inmates to reduce risk of an outbreak behind bars. Jail and prison populations are vulnerable to COVID-19 infections because close living quarters and group meal outings make social distancing nearly impossible, inmate advocates say.

Without swift action, Woods said, Santa Rita Jail could face catastrophic levels of infections seen at other large jails across the country. At least 287 inmates and 406 staffers tested positive for the virus in New York City jails, and in Chicago, the Cook County Sheriff’s Office reported that 238 inmates and 115 staff members had tested positive, according to the New York Times.

“It’s ridiculous that we still have people in custody serving short county jail sentences,” Woods said. “I understand most of them made plea deals and agreed to serve that time. But this virus has changed everything.”

So far, infections at Bay Area lockups have been minimal in comparison. There are no confirmed cases among inmates at San Francisco or Napa County jails, and two reported at Santa Clara County Main Jail. One of those two has since been released, and the other is isolated in an infirmary.

Sgt. Ray Kelly, a spokesman with the Alameda County Sheriff’s Office, said further releases must be balanced with the public safety of the community.

The jail population has already dropped by 671 inmates since the shelter-in-place order took effect, from 2,650 on March 16 to 1,979 on Thursday.

Those remaining include 486 federal inmates, and about 130 people who will qualify for release under a statewide order from California judicial leaders that reduces some offenders’ bail to $0.

Kelly said 1,381 inmates are awaiting trial on felony charges, and 90% of the alleged crimes were felonies that were violent or sexual in nature. Approximately 256 people are being held on murder charges.

“There’s certain individuals who are in jail who should never get out of jail based on charges against them,” Kelly said. “We have everything from serial killers to serial rapists. ... If they were to be released, they would pose a serious threat to public safety.”

Megan Cassidy is a San Francisco Chronicle staff writer. Email: megan.cassidy@sfchronicle.com Twitter: @meganrcassidy