Law enforcement officials would not discuss specific security measures being taken at the ports of entry, along the border or in the city of El Paso.
"We received credible information that drug cartels in Mexico have given permission to hit targets on the U.S. side of the border," El Paso police spokesman Officer Chris Mears said.
Authorities learned of the threat last week.
U.S. Customs and Border Protection Chief Officer Rick Lopez said: "CBP is on heightened alert ever since we became aware of the threats in Mexico."
U.S. Border Patrol spokesman Doug Mosier said officials "are reinforcing the importance of vigilance."
Drug cartel violence has claimed thousands of lives in Mexico this year. Nearly 800 people have been killed in Ciudad Juarez, a hardscrabble city of about 1.3 million people across the Rio Grande from El Paso.
The cartels, battling one another and the Mexican government for supremacy and control of lucrative drug and human smuggling routes, have become brazen in their attacks in recent months.
In Juarez this month, masked gunmen stormed a drug and alcohol rehabilitation center and killed eight people. Days later, Red Cross workers stopped treating gunshot victims for several hours after receiving death threats over Red Cross radios. The Red Cross had already stopped responding to emergency calls after 10 p.m. because of security concerns.
Law enforcement officials this year in New Mexico and Texas said they had received a purported cartel hit list identifying 15 to 20 potential targets in those states. Mears said the latest threat contained no specific targets.
The deadly wave of shootings and a rise in kidnappings for ransom in Mexico has prompted some of its citizens, including police officers and a prosecutor, to seek asylum in the U.S.
While the ongoing cartel war has been largely contained in Mexico, more than two dozen gunshot victims have been taken for medical treatment in El Paso, prompting security lockdowns at the county hospital.
Lopez said agents working at the ports, where those gunshot victims have been taken before coming into the U.S., are taking extra security precautions. Ambulances transporting gunshot victims are already being escorted by local law enforcement to the hospital, he said.