Tropical Storm Bonnie was upgraded to a category one hurricane on Sunday as it swept towards Mexico after killing three people in El Salvador and Nicaragua, the US National Hurricane Center said.

The hurricane, the third of the season off Mexico's coast, is carrying maximum sustained winds of 80 miles (125 kilometers) per hour "with higher gusts," the NHC said, citing satellite images.

"The core of Bonnie is expected to remain south of, but move parallel to, the coast of southern and southwestern Mexico during the next couple of days," the center said in its latest advisory.

Before moving towards Mexico, the storm caused damage to property in the Central American countries of El Salvador and Nicaragua, felling trees and flooding rivers, streets and hospitals.

A 24-year-old woman died in El Salvador, emergency services said, while in Nicaragua the army said a 40-year-old man was swept away trying to cross a river and a 38-year-old man died trying to rescue passengers from a bus.

Rescuers in El Salvador were still searching Sunday evening for a missing man and the search efforts will continue on Monday, the country's civil protection agency said.

"Bonnie generated very heavy rains and thunderstorms in the coastal area, the volcanic mountain range and the San Salvador metropolitan area, with strong gusty winds and hail in some areas," the environment ministry said.

El Salvador's President Nayib Bukele said all classes would be suspended Monday.

Bonnie, which made landfall in Nicaragua overnight Friday to Saturday, is set to drench southern Mexico with heavy rain, the NHC said.

Swells caused by the hurricane are to "cause life-threatening surf and rip current conditions," its advisory said.