MEXICO CITY, June 4 (Reuters) - Mexican soldiers on an offensive against drug gangs shot and killed three children and two women, a rights official said on Monday, as critics warn of mounting abuses in an army crackdown on cartels.

Soldiers manning a makeshift roadblock in the state of Sinaloa shot over a dozen times on Saturday at a car carrying two female teachers, a husband and wife and four children, said Oscar Loza, the state's top human rights official.

All the passengers were apparently unarmed, he said.

Since taking office in December, President Felipe Calderon has sent an unprecedented 25,000 troops to crime hot spots like Sinaloa to help corrupt and weak police forces tackle powerful cartels.

One child, a teacher and a man survived the shooting but are all injured, said Loza, who visited the La Joya de los Martinez village where the attack took place at the weekend.

"The man lost his whole family," he said. "It would be illogical that a father, traveling with women and his children, would confront the army and put at risk his family."

The army said it was not immediately able to comment on the shooting.

Calderon's muscular approach has won praise from Washington and is supported by many Mexicans fed up with a wave of gang violence that claimed about 1,000 lives so far this year, but opposition politicians and rights activists warn the use of soldiers in crime fighting leads to abuses.

Sinaloa state is home to the Sinaloa Cartel, headed by Mexico's most wanted man, Joaquin "Shorty" Guzman, who is in a turf war against the rival Gulf Cartel.

Calderon met Italian Prime Minister Romano Prodi on Monday. Prodi promised to share experiences from Italy's war against mafia groups but insisted Calderon upheld human rights.

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