A pandemic-related health order has contributed to a surge in border crossings.

Responding to news of the migrant deaths near the southern Texas border, Gov. Greg Abbott pointed the blame at what he said were President Biden’s “open border policies.”

Technically, the border remains sealed off to most migrants under a health order imposed in the early days of the pandemic that was designed to stem the flow of the coronavirus. But the policy, known as Title 42, has had the unintended effect of encouraging people to enter the country illegally more than once.

Since it was first put in place in March 2020, the order has allowed border agents to swiftly expel most migrants without giving them a chance to apply for asylum under the justification that it was for pandemic safety. Many are often sent back to Mexico without facing criminal penalties or detention, leading some to repeatedly try to cross the border. The uneven application of the rule — some families and unaccompanied minors are still being processed for asylum — has encouraged others to again enter the United States.

About three out of 10 adults attempting to cross have done it more than once, officials say, and some of them have tried as many as 10 times.

Under Mr. Biden, the Trump-era policy has been used to turn away at least a million people. His administration had sought to lift the order in May, but a federal judge issued a ruling requiring the administration to continue enforcing the measure. Some public health experts had criticized the order remaining in force, saying there was little scientific basis for it now that vaccine availability is widespread.

Homeland Security officials said that they had been bracing for as many as 18,000 migrants arriving daily should the policy end.

During the 2021 fiscal year, undocumented migrants were caught a record-breaking 1.7 million times. By May of this year, that number had already surpassed 1.5 million with four months remaining in the fiscal year.

Mr. Biden has also sought to end a policy commonly known as “Remain in Mexico,” which requires migrants from a third country arriving through the southern border to await the outcome of their asylum application in Mexico. The policy is now before the U.S. Supreme Court after states sued to stop the Biden administration from ending the program.

The two policies mean despite that Mr. Biden’s campaign pledges for a changed approach to migrants, border controls remain the largely same as they were under President Trump.