Six people who were killed when the SUV they were in crashed following a police chase were being transported by a smuggling organization, federal officials said Thursday.

The driver, a U.S. citizen, and two others in the vehicle are believed to be members of the smuggling organization, Leticia Zamarripa, a spokeswoman for U.S. Immigration and Customs Enforcement, said in a statement.

The driver was one of the individuals who died in the accident, while the other five killed were immigrants in the U.S. illegally.

Officials say the vehicle was packed with the three smuggling ring members and 13 people who were in the country illegally.

Those being smuggled in the vehicle were adults from Honduras, Guatemala and Mexico, Zamarripa said. One of the smuggling suspects is from Mexico, and the nationality of the other is unknown, she said.

The chase began early Thursday as officers in Edna, 90 miles southwest of Houston, tried to stop the 2003 Ford Explorer for a traffic violation, said city police Chief Clinton Wooldridge.

As the vehicle veered onto Highway 59, the driver seemed to overcorrect and the SUV flipped several times, police said.

Four people died at the scene and two more died at hospitals, Wooldridge said.

"It is a tragedy and it is a horrible situation," Wooldridge said at a news conference Thursday afternoon.

Two of the immigrants were being treated at a hospital in nearby Victoria for fractures, while another was in critical condition at a Houston hospital, Wooldridge said. The other immigrants who were injured in the crash were treated at Jackson County Hospital in Edna and later released into the custody of U.S. Border Patrol agents.

Two people who ran from the scene were tracked down and detained. A third person was found around 3 p.m. Thursday across the roadway from the crash site, near a home, Wooldridge said.

"We've been in contact with consulates and they are working with the medical examiner's offices to try and find these people's families," he said.

The car had been modified so it would hold 16 people, with the center seat having been removed, Wooldridge said.

"I believe the Ford Explorer is built on a half-ton chassis and it had ¾ of a ton of people. So that probably had something to do with the instability of the vehicle," he said.

It is not uncommon for vehicles packed with immigrants who have entered the U.S. illegally to be involved in deadly crashes as they are shuttled away from the border.

Last year, a South Texas teenager was sentenced to 20 years in prison after being convicted in a 2012 accident that killed nine immigrants. The teenager had been fleeing Border Patrol agents when the van he was driving with at least 17 immigrants inside flipped. Also, a Mexican man was sentenced to 45 years in prison over a crash that left seven immigrants dead in 2013.

Wooldridge said his agency and others in the area have a lot of experience stopping northbound vehicles that are transporting drugs and immigrants in the country illegally.

"That's fairly common in our area," he said.