Its maximum sustained winds have decreased to near 35 mph (55 kph), and it will likely dissipate later Monday over Mexico's mountainous terrain.
Even though Sonia is weakening, heavy rains are still possible in Sinaloa, western Durango and southern Chihuahua, the center said.
The government of Sinaloa state said classes were canceled for Monday in five municipalities that could be affected by the storm. Sixty shelters were being opened in case anyone had to evacuate their homes.
In the resort town of Los Cabos in Baja California, officials opened a shelter for possible evacuees and said the port had been closed to small craft.
The hurricane center said the storm could produce up to 6 inches (about 15 centimeters) of rainfall in Sinaloa and Durango states, with isolated areas getting as much as 10 inches (25 centimeters). These rains could produce flooding and mudslides, warns the National Hurricane Center in Miami.
In September, Mexico suffered its worst flooding since records began when storms Manuel and Ingrid converged from the Pacific and the Gulf of Mexico, killing more than 150 people and causing damage estimated at around $6 billion.
Last month, Hurricane Raymond caused some flooding as it approached the Pacific resort cities of Acapulco and Zihuantanejo, but no deaths or major damage was reported.
Sonia is the eighteenth named storm system during the current eastern Pacific hurricane season, which began in May and is set to conclude at the end of this month.
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