(CNN) -- Two police officers were fatally shot and another two were wounded Thursday in two separate shootings allegedly by the same suspects in West Memphis, Arkansas, police said.

The two suspects, who were using an assault weapon, were themselves fatally shot, said Inspector Bert Shelton, who is assigned to city hall for the West Memphis Police Department.

The incident began around 11:36 a.m. (12:36 p.m. ET), when West Memphis patrolman Bill Evans made a traffic stop on a white minivan traveling eastbound on I-40 at Airport Road, said Bill Sadler, public information officer for the Arkansas State Police.

After the vehicle exited the Interstate onto an off-ramp near College Avenue, Sgt. Brandon Paudert arrived on the scene as backup, Sadler said.

"It is our belief that Officer Evans was shoved to the ground by one of the suspects in the minivan and gunfire was directed at both officers," Sadler said.

The suspects then fled, driving east in the minivan, leaving one man dead and the other fatally wounded.

Within minutes, officers from other agencies -- including the Arkansas State Police and the Arkansas Fish and Game Commission -- began to converge on the area, looking for the suspects, he said.

About 90 minutes later, a minivan believed to be the one that had been seen leaving the shooting site was spotted in a parking lot of a nearby Wal-Mart, Sadler said.

There, it was approached by Crittenden County Sheriff Dick Busby and Chief Enforcement Officer W.A. Wren, who were traveling in the same vehicle, he said.

Both men were wounded in a gunbattle initiated by the suspects, who were using a long rifle and a handgun, Sadler said.

The gunbattle ended after "a very brave, young wildlife officer in his state truck rammed the suspect vehicle, preventing an exit of the suspects," who were killed, Sadler said.

Both wounded officers were taken to Regional Medical Center at Memphis, where they were in critical condition, said hospital spokeswoman Vivian Crawford.

Authorities would not identify the suspects, saying doing so could affect the integrity of the investigation.

Paudert was the son of Police Chief Bob Paudert, said West Memphis Police Department Assistant Chief Mike Allen.

Both of the dead officers leave widows and young children, he said. Paudert was 39, Evans was 38.

The FBI's evidence-response team was among the agencies involved in the investigation.

In a statement posted on his website, Arkansas Gov. Mike Beebe said Paudert and Evans "died upholding their duty to serve and protect the residents of West Memphis." He added, "This is a loss shared by all Arkansans."

A woman who answered the phone at the Wal-Mart Supercenter in West Memphis said the store, which is usually open round the clock, was closed after the incidents, and that store officials hoped to reopen by midnight (1 a.m. ET).