Three U.S. residents and seven other suspects arrested in a deadly shootout just across the border from Texas are members of the powerful Gulf drug cartel, Mexican officials said.

The gunfire, which left three people dead, broke out around noon Monday when Mexican federal agents chased a van full of people carrying assault weapons in the town of Rio Bravo, across the border from Donna, Texas, according to a government statement.

The army and federal police sent reinforcements after the suspects took shelter and began detonating grenades, Federal Public Safety assistant secretary Jose Patricio Patino told reporters Tuesday.

"The armed group that clashed with federal agents yesterday belonged to a cell of the Gulf cartel," Patino said.

Witnesses described a frightening scene with gunmen breaking down doors and positioning themselves inside homes for the gunbattle, which took place in front of the Rio Bravo police station, The McAllen Monitor reported.

Three suspected criminals were killed in the shootout, and five soldiers and five federal police officers were injured.

Ten people were arrested including three suspects from the U.S., identified as Ricardo Zamora Lopez, 32, and Jose Raul Gonzalez Sanchez, 30, both of Detroit, Michigan; and Esteban Valdez de los Santos, 30, of Texas, according to the statement.

Authorities did not release Valdez's hometown or identify the nationality of the other suspects. A heavily armed group of federal agents transported the 10 suspects to the capital on Tuesday.

At the news conference, Patino spoke only of two suspects from the U.S. and said the pair likely had strong criminal links on Mexico's side of the border. He added that police intelligence does not suggest a direct link between the Gulf cartel and any U.S. criminal organization in the Detroit area.

In a second shootout Tuesday evening, two federal agents were killed and three more injured when they clashed with a group of suspects in the nearby city of Reynosa, according to a Public Safety Department statement.

Local newspapers showed grisly photographs of what looked to be federal agents lying in pools of blood.

Drug violence has plagued Rio Bravo, about 15 miles south of McAllen.

The surrounding Tamaulipas state is the base for the Gulf cartel, one of Mexico's most powerful and brutal trafficking gangs. Authorities hold it responsible for much of the bloodshed along the Mexican border with Texas.

U.S. investigators say that at its height, the Gulf cartel had cells in Houston, Chicago, Atlanta and other U.S. cities and moved tons of cocaine per month into the United States.

The reputed kingpin of the Gulf cartel, Osiel Cardenas, was imprisoned in 2003, and has been extradited to the United States.