Police in Laredo, Texas, were evacuating people in low-lying areas as the rain-swollen Rio Grande rose to more than 25 feet (7.6 meters) above flood stage.
Tens of thousands of people already had been forced from their homes in Mexican towns as officials dumped torrents of water into flood-swollen rivers to avoid the risk of dams overflowing out of control due to last week's Hurricane Alex and its aftermath.
The U.S. National Hurricane Center in Miami said a new tropical depression was headed for the region and it could bring another 4 to 8 inches (10 to 20 centimeters) of rain, as well as possible tropical-storm-force winds.
By dawn Thursday, the storm was centered about 80 miles (130 kilometers) east of Brownsville, Texas, and was moving to the northwest at about 15 mph (25 kph).
A tropical storm warning was in effect for the Texas coast south of Baffin Bay and for Mexico north of the San Fernando River.
Hurricane Alex, unusually water-heavy, devastated the major Mexican city of Monterrey, and more than 100,000 people were still without water service this week. At least 12 people died in the flooding, according to Nuevo Leon state officials.
The hurricane's remnants caused rivers to rise across the area, forcing evacuations in Del Rio, Texas, some 110 miles (180 kilometers) upstream from Laredo, as well as in the Mexican state of Coahuila, where officials said some 10,000 homes had been damaged.
To the southeast, Mexican officials evacuated nearly 18,000 people from houses in Ciudad Anahuac for fear that water would overflow the Venustiano Carranza dam and threaten lives.
An airplane on an inspection tour of the flood zone crashed Wednesday, killing the mayor of the border town of Piedras Negras, the state public works director, a municipal civil defense official, a government photographer and the pilot and co-pilot.
Water behind the binational Amistad Dam on the Rio Grande already was at its highest level since 1974, according to the International Boundary and Water Commission, forcing officials to release water from it at the fastest rate in a quarter century.
The commission said the downstream Falcon dam would probably reach capacity within the next few days, suggesting future releases there will raise water levels along the river's lower reaches.
Much of that downstream area is protected against flooding by levees, but Mexico's National Water Commission said it was worried about low-lying settlements, most built by poor people without official permission.