Officials from both the U.S. and Mexico said Monday that four Americans who went to Mexico last week to get medical care were caught in a deadly shootout and taken by heavily armed men who put them in the back of a pickup truck.

On Friday, the four were travelling in a white minivan with license plates from North Carolina. The F.B.I. said in a statement Sunday that they were shot at soon after entering the city of Matamoros from Brownsville, which is at the very southern tip of Texas near the Gulf Coast.

The F.B.I. said that armed men put all four Americans in a car and drove them away from the scene. The FBI is offering a reward of $50,000 for the return of the victims and the capture of the people who took them.

Zalandria Brown of Florence, South Carolina, said she has talked to the FBI and local officials since finding out that her younger brother, Zindell Brown, is one of the four people killed.

In a phone interview, she said, “This is like a bad dream you wish you could wake up from.” “It is just unbelievable to see a family member thrown in the back of a truck and dragged.”

Ms. Brown said that her brother, who lives in Myrtle Beach, and two other friends went with a third friend to Mexico so that she could get a stomach tuck.

A video posted to social media on Friday showed four people being put into the bed of a white pickup truck by men with assault rifles and body armour. One of them was still alive and sitting up, but the others looked like they were either dead or hurt. At least one person looked like he lifted his head off the ground before being pulled to the truck.

The scene showed the terror that has been going on for years in Matamoros, a city in the state of Tamaulipas where different parts of the powerful Gulf drug cartel often fight with each other. Only in the state of Tamaulipas have thousands of Mexicans gone missing because of the violence.

On Monday, Mexico’s President Andrés Manuel López Obrador said, “There was a fight between groups, and they were arrested.” He did not give any more details. At first, he said that the four Americans were in Mexico to buy medicine.

Irving Barrios, the top prosecutor in the Mexican state of Tamaulipas, told reporters that a Mexican woman had died in the shootings on Friday.

Friday, there were so many gunfights in Matamoros that the U.S. Consulate sent out a warning about the danger and local authorities told people to stay inside.