Two of four US citizens kidnapped by gunmen after they drove into northeast Mexico have been found dead, and the two survivors have returned to the United States, the local government says.

"Of the four, two of them have died, there's one person injured, and the other person is alive," Americo Villarreal, governor of the border state of Tamaulipas where the four crossed into, said on a call with Mexican President Andres Manuel Lopez Obrador as the latter held a daily news conference.

Later, Tamaulipas' Attorney General Irving Barrios said on Twitter that the two surviving US citizens had been handed over to US officials at the border with Texas.

A Mexican official told Reuters the lone woman in the group was not injured.

The kidnappings have put a harsh spotlight on US concerns over widespread gang violence in Mexico.

Republicans, in particular, have been pushing for the US government to take a tougher line on organised crime south of the border amid rising overdose deaths caused by fentanyl, a synthetic opioid trafficked by Mexican cartels.

Republican Senator Lindsey Graham on Monday said it was time to "put Mexico on notice," and advocated introducing legislation to classify some Mexican drug cartels as "foreign terrorist groups" and set the stage to use military force if necessary.

"I would tell the Mexican government if you don't clean up your act, we're going to clean it up for you," he told Fox News.

US broadcaster ABC News on Monday named the four US citizens as Shaeed Woodard, Zindell Brown, Latavia "Tay" McGee and Eric James Williams - with the last two named by a Tamaulipas official as the survivors.

Williams was receiving treatment in hospital in Brownsville, Texas, which is across the border from Matamoros, the city in Tamaulipas where the four had entered Mexico, the official said.

CNN said one of the four US citizens was seriously injured.

The four US citizens were in a white mini-van when they entered the border city of Matamoros on Friday.

Gunmen fired on the passengers shortly after they crossed into Mexico and then herded them into another vehicle before fleeing the scene, according to the US embassy in Mexico.

A Mexican bystander was also killed when the abduction took place, authorities said.

US media have reported that McGee was travelling with the group to Mexico to get cosmetic surgery.

Lopez Obrador expressed his "sincere condolences" and said one person was in custody over the kidnapping in Tamaulipas, which has long been one of the most violent, gang-ridden states in Mexico.

He pledged to bring the perpetrators to justice.

But he lashed out at what he cast as "tabloid" coverage of the incident, and accused the media of not giving the same attention to killings of Mexicans in the United States.

US Attorney General Merrick Garland also offered his condolences and said he had been briefed by the FBI on the matter.

He did not comment on reports of the deaths.

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