Officials in Texas' big cities say their public testing sites are being strained. Austin has begun to limit who can be tested.

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As the new coronavirus continues to spread in Texas, leaders of some of the state's biggest cities said Monday that their testing sites were being strained, forcing them to turn away people in the middle of the day or limit who is eligible to take a test.

In Travis County, interim County Judge Sam Biscoe said the county’s public testing is being rationed to only people with symptoms. Previously, local leaders had encouraged anyone to get tested, including asymptomatic people and people that had come into contact with COVID-19 patients.

“The rapid increase in cases has outstripped our ability to track, measure, and mitigate the spread of the disease,” Biscoe wrote in a letter to Gov. Greg Abbott asking to allow metropolitan areas to issue their own stay-at-home orders.

The largest laboratory analyzing tests is also strained, Biscoe said, to the point that the county has decided to prioritize cases from severely ill patients in hospitals. Residents in Travis County who don't show symptoms still have other options, like private facilities, to get tested.

In Houston, Mayor Sylvester Turner said his city's two public testing sites, where testing is still available to people who are symptomatic or asymptomatic, reached their maximum capacities before noon.

“The capacity on those sites will be increased from 500 [daily tests] to 650 each,” Turner said. “It is clear that there is a demand out there, and we need to ramp up as best as we can to meet that demand.”

Meanwhile, the two community-based testing sites in the city of Dallas are reaching their capacity "by noon or early afternoon daily," according to city spokesperson Roxana Rubio. In these sites, testing is restricted to symptomatic patients, high-risk people, first responders, essential workers and asymptomatic patients who have engaged in large group settings.

The shortages come even as testing has ramped up in recent weeks. In April, Abbott set a goal of 30,000 daily tests in the state — a benchmark it consistently missed through the first half of June. The state has more frequently met that goal lately, but the increased number of tests is being accompanied by an added demand as the virus spreads.

Community testing sites have seen increasingly long wait times as more than 38,000 positive cases were reported in the last week in Texas. The city and county sites are part of a longer list of options Texans have to get tested. The Texas Department of State Health Services has created a statewide map with these facilities, which also includes scores of private sites.

Correction: An earlier version of this story misspelled the name of interim Travis County Judge Sam Biscoe.