(Updates with details on grenade, background)

MONTERREY, Mexico, Jan 6 (Reuters) - Gunmen threw a grenade and opened fire outside a television news station during its evening broadcast in Mexico on Tuesday and left a message warning journalists from reporting on drug war violence.

Gunmen hurled the grenade at the regional studios of Mexico's top broadcaster Grupo Televisa in the northern city of Monterrey during the evening news show, the station's reporters said live on the air.

No one was hurt in the attack, believed to be the first against a TV station in Mexico, and in which the gunmen sprayed one of the complex's outside doors with bullets. The grenade exploded in a studio workshop used to build sets.

Gunmen also left a handwritten message on a car bumper near the studio that read: "Stop reporting just on us. Report on the narco's political leaders," in a apparent reference to the Mexican government.

Mexico is facing spiraling violence between warring drug gangs and the army in a battle that killed some 5,700 people last year.

Attacks on the media have mounted since President Felipe Calderon launched his military assault on cartels at the end of 2006. Suspected drug hitmen shot dead a crime reporter in the border city of Ciudad Juarez in November.

Since 2006, 15 journalists have been killed in Mexico, making it one of the world's most dangerous countries for the media, according to the U.S.-based nonprofit organization Committee to Protect Journalists.

Monterrey, a prosperous manufacturing and services city close to the U.S. border, was mainly calm in the drug war last year, but the powerful Gulf cartel and its feared Zeta hitmen run drugs through the area to Texas.

In October, gunmen shot at the U.S. consulate in Monterrey and threw a grenade that did not explode. (Reporting by Robin Emmott, editing by Vicki Allen)

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