Roadblocks are a frequent tactic of Mexico's drugs gangs in their fight against the security forces
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Mexican police have been involved in fierce gun battles with suspected drug traffickers blockading the main roads into Morelia, the capital of Michoacan state.
There has also been fighting in the nearby city of Apatzingan.
At least three people were killed, including an eight-month-old baby apparently caught in the crossfire.
Michoacan, in western Mexico, is a stronghold of a powerful drugs cartel known as La Familia Michoacana.
The five main roads leading in and out of Morelia were blocked by burning cars and buses, police said.
Gunmen fired into the air to force drivers and passengers out of their vehicles before setting them ablaze.
Schools kept children inside their classrooms for their protection, and the city's university was closed, the Mexican newspaper El Universal reported.
Fighting broke out as police moved in to clear the blockades.
The upsurge in violence in Michoacan began on Wednesday when federal police went into the city of Apatzingan to search for suspected La Familia gang members, police said.
They quickly came under fire with automatic weapons, and police reinforcements were also attacked as they drove to assist their colleagues.
Army troops and helicopters were also brought in, and the cartel gunmen retreated, blocking the road behind them with burning vehicles.
One police officer was killed along with two civilians - a baby and a young woman.
Mexico's public security ministry denied local media reports that a police helicopter was shot down during the fighting.
La Familia Michoacana is involved in cocaine smuggling to the US along Mexico's Pacific coast as well as the production of the synthetic drug, methamphetamine.
Despite a reputation for ruthless violence, it has always claimed strong links to the community in Michoacan state, and advocates religious and family values.
In recent months the gang has come under growing pressure from the Mexican authorities, with several suspected leaders captured.
It has also been involved in bloody territorial wars with rival cartels.
The cartel was recently reported to have offered to negotiate a truce with the government and disband.
Michoacan is the home state of President Felipe Calderon, and one of the first places where he deployed the army to fight drugs gangs after he took office in 2006.
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