The Barrio Azteca gang "most definitely" has ties to gangs in Mexico, he said.
The gang is said to operate on both sides of the US-Mexico border in conjunction with drug cartels.
However, Payne did not say how many suspected gang members had been detained in the raids.
Lesley Enriquez, an American working at the consulate in Ciudad Juarez; her American husband, Arthur Redelfs; and Jorge Alberto Salcido, the Mexican husband of another US consular employee, were killed in ambushes just minutes apart last week after leaving a birthday party in the Mexican city.
Police officers detained
The Texas raids came at the same time as Mexican authorities on the other side of the border detained two-thirds of the police force in the northern town of Villaldama, for suspected ties to drug cartels.
Erasmo Villarreal, a local official, told the Associated Press that the marines arrested eight of the 12 officers on the force.
Villaldama is a town of about 4,000 people near the city of Monterrey in the state of Nuevo Leon.
Javier Trevino, the state secretary-general said the town's police chief was among those arrested on Wednesday.
Felipe Calderon, the Mexican president, has been waged an aggressive campaign to eliminate corruption from municipal police forces, and hundreds of police across the country have been arrested or fired for alleged ties to criminal gangs.
The military has led many of the arrests, and in some towns, army officers have taken over as police chief.
The arrests in Villaldama came two days after scores of police officers in other regions were detained in probes into a wave of drug-related killings and kidnappings.