(corrects spelling of "grisly" in fifth paragraph)

MEXICO CITY, May 7 (Reuters) - Mexican soldiers backed by helicopters killed four drug gang members in a shootout on Monday that lasted almost two hours in a western state at the heart of President Felipe Calderon's war on drug gangs, police said.

Terrified neighbors fled the streets in the town of Apatzingan as more than 300 soldiers battled gunmen holed up in a house and deployed throughout the town.

Masked cartel members killed five soldiers in an attack in the region last week, one of the heaviest blows to the military since Calderon sent thousands of troops to tackle drug gangs across Mexico last December.

One of the dead on Monday was a woman, Michoacan state authorities said.

Despite Calderon's campaign, execution-style killings and other grisly murders have gone on unabated.

Drug-related killings in Mexico number more than 700 so far this year, compared to 2,000 in 2006. Michoacan, a mountainous avocado-growing area, is one of the states worst hit.

In one notorious incident, drug hitmen rolled five severed human heads onto a dance floor in a Michoacan town in a warning to rivals.

On Saturday, gunmen killed a police chief in the southern state of Chiapas, while a police chief in the Caribbean resort of Cancun survived an attempt on his life earlier last week.

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