Houston saw its number of confirmed COVID-19 cases more than triple Saturday, ballooning from 69 to 232 as testing revealed more cases, but Mayor Sylvester Turner warned that efforts to further increase testing have been stymied by the federal government.

Turner announced the surge along with the city’s second coronavirus-related death — a woman in her 70s who had underlying health issues. He offered a sobering assessment that those statistics would continue to rise sharply.

“Let me just say, the testing has been limited. We know there are more cases,” the mayor said. “The way I look at it, I take 232 and I multiply by 10. Because we just don’t know.”

The city’s efforts to expand testing were dealt a blow Saturday when the federal government told Turner it would only send enough personal protective gear to conduct 250 tests a day in the nation’s fourth-largest city.

The plan, for weeks, has been to open two city sites that each can conduct 250 tests per day. One of those sites opened March 20, with help from the Federal Emergency Management Agency, and has conducted more than 1,500 tests, according to city health officials. The other has been held up due to delays in equipment shipments.

Now, the federal government says those shipments won’t come at all. According to Turner, the feds said any future expansions will have to be funded by local jurisdictions.

“That’s just unacceptable,” Turner said. “So we’re going to have to try to figure out how to work that out… We need robust testing in order to get a better measurement of the degree of community spread that exists in our city.”

FEMA didn’t respond to a request for comment.

Turner also said the city has eased restrictions and opened its lone testing site to anyone with symptoms. People can call 832-393-4220 to start the screening process. Harris County is operating two sites with FEMA, one in Katy and one in Baytown. Its screening process is online at readyharris.org.

Private labs, like hospitals and other health clinics, have more capacity locally and statewide. They have accounted for the vast majority of testing in Texas, conducting more than 22,000 of the 25,260 tests done in the state as of noon Saturday.

That testing, though still limited, has revealed a climbing number of cases.

Harris County announced an additional 53 positive tests Saturday in its unincorporated territory, giving it 445 with Houston included — the most of any county in the state. The grim distinction previously belonged to Dallas County.

The tally across the eight-county Houston region was up to more than 700 cases. Across Texas, there were nearly 2,500 as of Saturday night.

The Houston woman who died with the virus Friday was not identified. She was hospitalized at the time, and her positive test came back the same day she died.

The city’s first death occurred Tuesday. Another death was previously reported in Harris County. The death toll statewide is 28.

“We are saddened by the death of a second Houstonian,” said Dr. David Persse, Houston’s local health authority. “Our city unfortunately will likely see more deaths as this pandemic touches the lives of more people in our community.”

Meanwhile on Saturday, Texas Department of Public Safety troopers began screening airplane passengers landing in the state from New York, New Jersey, Connecticut and New Orleans.

Earlier this week, Gov. Greg Abbott ordered those people to self-quarantine for 14 days, though the order only applied to those arriving by plane. DPS said they would require the travelers to fill out a form with identifying information, including their names, dates of birth, phone numbers and where they will be quarantining.

The agency said its troopers would conduct random checks at those homes to confirm the people were quarantining. Violators could face fines up to $1,000 and 180 days in jail.

Turner, who has for weeks asked people traveling to Houston to voluntarily quarantine, said he wasn’t implementing any additional move for people who drive to the city from New Orleans, where a large outbreak is beginning to overwhelm that city’s healthcare system.

The mayor spent part of Saturday touring the city and gauging whether residents were following Harris County’s “Stay Home, Work Safe” order. That policy shuttered many non-essential businesses and asked residents to remain home save for essential work, critical errands or appropriately-spaced outdoor activities.

He said the city might soon fence off playgrounds and basketball courts in its parks, where maintaining a six-feet distance is more difficult.

“Quite frankly, in the end, it’s going to require the cooperation of everybody,” Turner said. “If it gets to the point, for example, that people are ignoring the request to engage in social distancing, then we have to take the next step.”

He didn’t specify what that would be.

Persse said the large, single-day spike in confirmed cases was caused by the need to reconcile reports coming in from various testing sites and laboratories. They want to make sure they're not duplicating people, ensuring they have an accurate count.

“The numbers give you some degree of what's taking place, but... the numbers are very fluid," Turner said.

The new tally of confirmed cases also includes three Houston police officers, bringing the total number in the department to seven.

Fire Chief Samuel Peña told the Chronicle one firefighter has tested positive for the virus, and he is recovering at home. Fifteen others are quarantined with symptoms. In all, 83 firefighters are in quarantine.

“We’re still waiting some tests and of those we have gotten back, none have been positive for COVID-19,” Peña said of the symptomatic group.

Staff writers Jordan Rubio and Sergio Chapa contributed to this report.