KILLEEN, Texas — The five metropolitan areas in the United States that now have the highest rate of new coronavirus cases relative to their population are all in South Texas, according to data compiled by The New York Times.

The communities all lie along the border with Mexico or on the Gulf Coast: Brownsville-Harlingen, Eagle Pass, Rio Grande City, Corpus Christi and Laredo.

Their numbers underscore the virulence of the virus in Texas, where officials have struggled to both keep the state open and curb infection. More than 300 deaths were announced on Wednesday in the state, which is approaching a total death toll of 10,000.

Representative Filemon B. Vela Jr., a Democrat whose district includes Brownsville and Harlingen, said that in late June he did not know anyone who had the virus. Now, he said, he knows hundreds. “In one day, I had four people who I knew die,” Mr. Vela said. “It’s just a really bad situation.”

Four of the five metro areas with the worst death rates in the country over the last two weeks were also in the South Texas border region — Rio Grande City, Brownsville-Harlingen, McAllen and Eagle Pass. The fifth was Payson, Ariz. In Rio Grande City in rural Starr County, which has only one overwhelmed hospital, the death rate was the highest, at 0.68 per 1,000 people.

In Laredo, health officials called it a crisis. Hospitals have been at or near capacity every day. The state turned a local Red Roof Inn into a 106-bed temporary hospital for coronavirus patients with mild cases, but local leaders have been urging officials to allow patients with more serious cases in.

The city’s five nursing homes have had 40 virus-related deaths. Officials were stunned by the citywide death toll of 102 in July, but with the number of deaths for August already at 57, they expect to surpass that this month.

“We see an unprecedented amount of death in the history of Laredo,” said Dr. Victor Treviño, the top health official in the city. “When the state opened, that’s when we saw the infection rate increase dramatically.”

Mr. Vela and other congressional Democrats in Texas have criticized Gov. Greg Abbott’s handling of the state’s reopening. When Mr. Abbott, a Republican, reopened the state in phases beginning May 1, he lifted the state’s stay-at-home order and prohibited local officials from adopting their own. After cases increased, Mr. Abbott paused the reopening, ordered bars to close and issued a statewide mask mandate for most Texans.

“Shutting down the bars isn’t enough,” said Mr. Vela, who called on the governor on Thursday to issue stay-at-home orders in hard-hit counties or allow local officials to put them in place.

On Thursday, Mr. Abbott met with officials in the West Texas city of Lubbock and warned the public about what he called “Covid fatigue.” In remarks to reporters, he urged Texans to continue to wear masks and practice social distancing. He was without a mask as he spoke, sitting near several local officials at an indoor news conference.

“If people do not continue to, in a very disciplined way, maintain the highest level of standards, what you will see is an acceleration of the expansion of Covid-19,” the governor said.

The virus has had a scattershot effect in Texas, with some regions seeing rising numbers and others reporting a decrease in cases.