A group of four US citizens who travelled to Mexico last week to seek health care got caught in a deadly shootout and were kidnapped by heavily armed men, according to officials from both countries.

The four were travelling on Friday in a minivan with North Carolina license plates. They came under fire shortly after entering the city of Matamoros from Brownsville, at the southernmost tip of Texas near the Gulf coast, the FBI said in a statement on Sunday.

"All four Americans were placed in a vehicle and taken from the scene by armed men," the FBI said. The bureau is offering a $50,000 reward for the victims' return and the arrest of the kidnappers.

Zalandria Brown of Florence, South Carolina, said she has been in contact with the FBI and local officials after learning that her younger brother, Zindell Brown, is one of the four victims.

Ms Brown said her brother and two others had accompanied a friend who was going to Mexico for a tummy tuck surgery.

A video posted to social media showed men with assault rifles and body armour loading the four people into the bed of a white pickup in broad daylight. One was alive and sitting up, but the others seemed either dead or wounded. At least one person appeared to lift his head from the pavement before being dragged to the truck.

Mexican President Andres Manuel Lopez Obrador said Monday that "there was a confrontation between groups, and they were detained," without offering details. He said earlier the four Americans came to Mexico to buy medications.

Tamaulipas' chief prosecutor, Irving Barrios, told reporters that a Mexican woman died in Friday's shootings. He did not specify whether she was killed in the same gunfight where the kidnapping took place.

Shootouts in Matamoros were so bad on Friday that the US Consulate issued an alert about the danger and local authorities warned people to shelter in place. It was not immediately clear how the abductions may have been connected to that violence.

US Ambassador to Mexico Ken Salazar said in a statement Monday the Americans were kidnapped at gunpoint and an "innocent" Mexican citizen died in the attack. He said various US justice agencies were working with their Mexican counterparts to recover the missing persons.

The State Department warns US citizens not to travel to Tamaulipas. However US citizens who live in Brownsville or elsewhere in Texas frequently cross to visit family, attend medical appointments or shop. It's also a crossing point for people travelling deeper into Mexico.

Three US siblings disappeared near Matamoros in October 2014 while visiting their father and were later found shot to death and burned. Their parents said they had been abducted by men dressed in police gear identifying themselves as "Hercules," a tactical security unit in the city.