The meteorologists said that Willa was moving toward the northeast at speeds near 20 mph (32 kph), movement expected to continue during the next 12 hours.
Although Willa weakened from a Category 5 to a Category 3 hurricane on the five-step Saffir-Simpson scale Tuesday morning, the US National Hurricane Center still warned residents that the hurricane will bring a risky storm surge, wind and rain to western Mexico.
Willa, a Category 3 hurricane on the five-step Saffir-Simpson scale, veered inland near the town of Teacapan, about 60 miles (100 km) south of the coastal resort of Mazatlan in the state of Sinaloa, satellite images showed.
The U.S. National Hurricane Center said the storm's forward movement had sped up to 17 miles per hour (28 kph) late Tuesday and it was expected to rapidly weaken.
Emergency officials said they evacuated more than 4,250 people in coastal towns and set up 58 shelters ahead of the unsafe Category 3 storm, which was expected to blow ashore in the evening near Mazatlan, a tourist spot of high-rise hotels and about 500,000 people, many of them US and Canadian expatriates.
Classes across the state were suspended on Wednesday, Durango governor Jose Aispuro said on Twitter.
Willa weakened to a tropical storm early Wednesday as it ran into mountains, and is expected to be a rainmaker by the time it crosses the US-Mexico border.
Forecasters are concerned about storm surge and rainfall.
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Up to 18 inches (45 cm) of rainfall could pummel parts of the storm zone, the Miami-based hurricane center said. An aircraft with the Air Force Reserve's Hurricane Hunters was forced to turn around Monday over concerns for its onboard equipment after a lightning bolt from one of Willa's outer rain bands blasted it, according to the National Hurricane Center. A decree of "extraordinary emergency" has been set for 19 municipalities in Nayarit and Sinaloa states.
Farther south, meanwhile, Mexican officials reported 12 deaths related to heavy rains from Tropical Storm Vicente.
It was due to weaken fast as it moved inland, the National Hurricane Center (NHC) said.
Airlines have started moving out of Willa's path. Southwest Airlines has canceled all flights at the global airport in Puerto Vallarta, a resort city in Jalisco state.
Mexican emergency officials say they've evacuated more than 4,250 people in towns along the Pacific coast that are threatened by Hurricane Willa.
Mexico's Pacific coast has already been hit by deadly storms and rains this hurricane season.
While Hurricane Willa will not make direct contact with any American coast, the now Category 4 storm is believed to have a huge impact on weather patterns in the coming week.
Increasing numbers of major hurricanes, along with a greater propensity of storms to undergo "rapid intensification" are expected consequences of warmer ocean waters resulting from climate change.