Newton was "still strengthening" and packing maximum sustained winds of 65 miles (105 kilometers) per hour as the system churned toward the northwestern Baja California peninsula, a favoured destination of American tourists, the US National Hurricane Center said.
Newton is expected to grow into a hurricane at landfall in the state of Baja California Sur today, it added.
The Mexican government issued a hurricane warning for parts of the state.
For the Baja California peninsula, "winds are expected to first reach tropical storm strength by late tonight, making outside preparations difficult or dangerous," the Miami-based NHC said in a 1500 GMT bulletin.
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The center's 1800 GMT advisory put the storm at 440 kilometers south of Baja's Cabo San Lucas beach destination.
Newton was moving northwest at 24 kilometers per hour and causing tropical storm conditions in Manzanillo and other coastal areas.
The storm is expected to produce as much as 10 inches (25 centimeters) of rain in several Pacific coast states, which could trigger life-threatening flash floods and mudslides, the center said.
The weather system has already caused damage in the southwestern state of Guerrero, including its resort of Acapulco, over the weekend before becoming a tropical storm.
Torrential rains that began Saturday morning caused 33 landslides on highways in Guerrero.
The downpour also caused a road to collapse in central Acapulco, sending two cars falling downward and injuring at least three passengers, the authorities said.
Heavy rainfall trapped around 200 people in their housing complex, prompting air evacuations by police, marines and the army.
While western Mexico was getting hammered with precipitation, the United States was spared the worst when Tropical Storm Hermine crashed ashore in Florida -- a hurricane at the time -- before moving out to sea.
Located some 320 kilometers southeast of the eastern tip of New York's Long Island, Hermine packed sustained winds of 110 kilometers per hour and was expected to remain near hurricane strength yesterday.