Gov. Abbott has made crackdown on migrants central to his re-election campaign.

Gov. Greg Abbott of Texas, facing re-election for a third term in November, has positioned himself as the defender of the country from migrants, making his aggressive stance on unauthorized migration central to his political campaign, even though his policies have been ultimately unsuccessful in stemming the arrival of migrants.

Even though the federal government enforces immigration law, Mr. Abbott has poured billions into sending state police and the National Guard to the border, repurposed state prisons to hold migrants charged with trespassing and set up check points for trucks from Mexico, disrupting international trade.

His Democratic challenger, Beto O’Rourke, has criticized Mr. Abbott for staging “stunts” and failing to achieve any meaningful progress in his years as governor in resolving the situation at the border.

Hours before the discovery of the migrant deaths, he boasted on Twitter of the number of migrants apprehended and criminally charged under what he has dubbed “Operation Lone Star.”

Despite the arrests, more migrants have been arriving at the border and managing to evade detection and enter the country illegally. In March, federal agents recorded nearly 129,000 crossings into Texas, about 11,000 more than the same period last year, when Mr. Abbott began the operation.

After news of the deaths emerged, he pointed the blame at President Biden’s policies.

“These deaths are on Biden. They are a result of his deadly open border policies,” he wrote on Twitter. “They show the deadly consequences of his refusal to enforce the law.”

Mr. Abbott’s approach to fortifying Texas’ 1,254-mile border, constructing new fencing and threatening to declare an “invasion” to invoke war powers, helped him fend off primary challengers further to his right and has made him a regular on Fox News.

In April, he started paying for buses to ferry migrants from Texas to Washington, D.C. and drop them off at the steps of the U.S. Capitol.

Federal officials were expecting that the lifting of a pandemic-related emergency public health order, under which many migrants have been swiftly expelled, could bring thousands of migrants daily to the southern border, which has already been seeing a surge of illegal crossings.

The rule, Title 42, was set to be lifted in May, but a federal judge ordered that it remain in place. The Biden administration said it would appeal. It has used the rule more than one million times to turn migrants away.

Judges have also blocked Mr. Biden from canceling a Trump-era policy that requires many asylum seekers to remain in Mexico while their immigration cases are considered by U.S. courts.

Zolan Kanno-Youngs contributed reporting.