Cristina is packing maximum sustained winds of 120 kph (75 mph) and is now located 425 kilometers (265 miles) south of the city of Manzanillo, the Miami-based center said.
The hurricane is moving slowly west and is expected to gain strength over the next 48 hours.
The center said that swells spawned by the hurricane are hitting parts of south-central and southwestern Mexico.
The rough water will probably continue into the rest of the day and could cause life-threatening surf and rip current conditions, the center said.
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