Residents in Mexico’s northern state of Tamaulipas, across the Texas border, sighed in relief this weekend as they learned that Beryl would only bring moderate to heavy rains in a few locations. The storm was originally expected to make landfall in Mexico twice.

Still, authorities were taking no chances.

“Although the trajectory now may indicate that it is more focused on the Texas side, we ask not to be careless and not to let our guard down,” Héctor Joel Villegas González, the state’s government secretary, said in a news conference on Saturday. “Natural phenomena have no word of honor.”

Earlier in the week, officials in Tamaulipas set up temporary shelters, monitored dams, identified areas vulnerable to landslides and took steps to prevent potential flooding and road blockades — such as clearing the drainage and pruning trees.

Some people were heeding the authorities’ advice. René Aguirre Garza, who coordinates a residential neighborhood in Matamoros that has previously been affected by flooding, said some of his neighbors were placing sand bags around their houses and cleaning their streets.

Others were more carefree. Despite officials warning residents not to visit popular beaches facing the Gulf of Mexico, some beachgoers enjoyed the sun and the waves.

On Saturday, tourists, vendors and fishers strolled along Bagdad Beach in the municipality of Matamoros, unconcerned by the incoming storm. A few officials were urging people to go home, but residents replied that nothing would happen as Beryl was already moving north.

“We’ll see what happens,” said Francisco Gabriel Ponce Lara, a rescue coordinator with the Matamoros Red Cross. “As far as I know, we are only going to get about eight inches of rainfall.”

Just like it was no secret that Beryl would bring some much-needed rain to Texas, authorities in Tamaulipas also hoped the storm and the hurricane season would help end — at least temporarily — a historic and brutal drought in the state.

In May, before Tropical Storm Alberto drenched the northeastern coast of Mexico, about 97.7 percent of Tamaulipas was suffering from some degree of drought, according to the country’s meteorological service. In its latest report on Friday, the agency said that number had dropped to 16.3 percent.

“Water for our state has been a blessing because the dams have been empty,” Mr. Villegas González told reporters on Saturday, adding that a system of lagoons that provides water to thousands of locals “has recovered.”

According to the National Hurricane Center, a tropical storm warning was in effect on Sunday morning for the northeastern coast of Mexico.

Edyra Espriella contributed reporting from Matamoros, Mexico.