A gunman hijacked a US postal truck and opened fire at random in the US state of Texas on Saturday, shooting dead at least five people and wounding many others before dying in a shootout with officers.

Police identified the suspect as a white man in his mid-30s, but could not yet name him or say why he carried out the attack in the West Texas cities of Midland and Odessa.

Coming less than a month after a gunman killed 22 people in the Texas city of El Paso, the latest bloodshed immediately ignited fresh calls for gun control to stem the US scourge of mass shootings.

"We have at least 21 victims, 21 shooting victims and at least five deceased at this point in time," Odessa city Police Chief Michael Gerke told reporters.

Three police officers were injured, he said.

The Odessa Police Department had earlier reported that a suspect was "driving around Odessa shooting at random people" and "just hijacked a US mail carrier truck."

Troopers had initially tried to pull over a passenger vehicle on the Interstate 20 highway but before it stopped, "the male driver [and only occupant in the vehicle] pointed a rifle toward the rear window of his car and fired several shots toward the DPS patrol unit," the Texas Department of Public Safety said in a statement.

One trooper was wounded, the suspect fled the scene, "and continued shooting innocent people," the department said.

Some of the shots were fired on the highway linking the cities of Odessa and Midland, where cars were left with bullet holes. "I just found out a friend of mine passed away," David Turner, the mayor of Odessa where the incident ended, told Fox News.

"This coward pulls up beside" and opens fire on the car where the man and his family were waiting at a stop light, Turner said.

During his rampage, the suspect had switched vehicles by hijacking the postal van, and Gerke said he "would assume" the postal worker was among the victims.

Police said the suspect died during an exchange of fire with law enforcement at a movie theater in Odessa.

Alex Woods, a witness, told CNN that near the movie theater "I could see a bunch of gunfire going off. And I could see the officer walking up to the mail van and discharging his weapon into it. 

"And I believe that was when the shooter was killed."