MEXICO CITY, Aug 31 (Reuters) - Tropical Storm Henriette moved toward Mexico's Pacific coast on Friday, threatening the resort of Acapulco with rains and hilly areas with mudslides and flash floods.

The Mexican government announced a tropical storm warning from a remote national park in the coffee growing state of Oaxaca to the port cities of Manzanillo and Lazaro Cardenas.

The storm is expected to gather strength in the next 24 hours as it moves up the coast toward the Baja California peninsula, popular with U.S. tourists,

Henriette is expected to pass about 100 miles (160 km) off the peninsula's coast on Tuesday, according to the U.S. National Hurricane Center.

On Friday morning, the center of Henriette was about 85 miles (135 km) south of Acapulco, moving northwest with maximum sustained winds of some 40 mph (65 kmph), the hurricane center said.

"Life-threatening flash floods and mudslides are possible," the Miami-based center said.

Small villages and towns in the hills that rise behind many of Mexico's Pacific beach resorts are susceptible to landslides.

At least 10 people were killed when rains trailing Hurricane Dean pounded the country last week.

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