Roughly one in three people of Boston's homeless community have tested positive for the COVID-19 virus, Boston officials said Tuesday.

Boston Mayor Marty Walsh and Boston Health and Human Services Chief Marty Martinez shared the grim statistic at one of Walsh’s near-daily press briefings during the coronavirus crisis here.

“Right now, we think there’s about close to two hundred cases in the homeless community,” Martinez said. “We think that number is probably close to 30 percent of those who were tested.”

Walsh said the city has secured roughly 170 beds at a Suffolk University dormitory, and that they should have capacity for as many as 500 beds for people who are homeless at the Boston Convention Center, which is being re-purposed into a temporary field hospital, but which has not yet opened as such.

Walsh said he hoped the city could begin using the convention center for isolation and treatment by the end of this week.

A spokesperson for the city’s Public Health Council said the city does currently have isolation capacity for all positive COVID-19 cases among the city’s homeless population.

The news comes on the heels of at least one other reported outbreak among people staying in Massachusetts congregate homeless shelters, some which house hundreds of individuals in cramped quarters nightly. On Monday, The Brockton Enterprise reported that more than two dozen homeless shelter guests as well as several shelter staff, had tested positive for COVID-19 at the MainSpring House shelter in Brockton.

Shelter operators, state and local officials and advocates for the homeless have been calling for weeks for Governor Charlie Baker and state officials to act quickly — and with the weight of the state’s emergency authority — to secure or provide capacity to depopulate crowded shelters to prevent what they called likely or even inevitable outbreaks in such settings.

See more of WGBH News recent coverage on Massachusetts homeless shelters and coronavirus

“We’re not surprised that there’s an increasing number of people experiencing homelessness testing positive for COVID-19, given that the state’s main response to providing shelter … has been to place people in congregate settings where we know that the virus can spread easily,” said Kelly Turley of the Massachusetts Coalition for the Homeless.

The statistics reported in Boston, Brockton and elsewhere, Turley said, “are unfortunately probably the tip of the iceberg in terms of what’s coming up ahead.”

Turley praised efforts by Boston officials to secure such facilities locally; but said the Baker administration needs to step up for other communities around the state.

“We’re concerned that while there’s been discussions for several weeks there is still no concrete plan” by the Baker administration to do so, Turley said.

Jim Stewart, who runs the First Church Shelter in Cambridge, said shelter operators around the state have little or insufficient action by state or local authorities.

Stewart said local officials have promised quarantine facilities similar to those being employed in Boston — “but they’re not online yet.”

As far as state guidelines, he said, “as far as I can tell it’s, ‘Tell them to wash their hands, practice social distancing,’ … but social distancing in these places is practically impossible.”

Officials from state health and housing agencies did not immediately reply to a request for comment, but have said in recent days and weeks that state officials are working with local officials and shelter operators on the issue.

Recent guidance posted on website for the state’s Department of Housing and Community Development recommends shelter operators concerned about preventing an outbreak of COVID-19 “can work with their local emergency management director to set up an alternative shelter site or to stand up a tent next to their existing footprint.”

“They’re kicking it back to the nonprofits, folks who are already up to their eyeballs in challenges,” Stewart said, ”and saying ‘Well, you figure out how to make it work [politically] and we’ll throw up a tent for you.’”

Follow Isaiah Thomspon on Twitter