The National Hurricane Center in Miami said in a 2 p.m. PDT advisory Cosme was centered about 335 miles southwest of Manzanillo, Mexico, and about 575 miles south-southeast of Cabo San Lucas, Mexico.
Its sustained winds had revved up to 60 miles per hour, up from 50 mph at 8 a.m.
Because the storm was so far out to sea, there were no coastal watches or warnings in effect, though it is expected to generate life-threatening surf and rip currents along the Mexican coast from near Manzanillo to Cabo Corrientes Monday night and Tuesday, the hurricane center said.
Cosme was moving northwest at about 14 mph and was expected to turn to the west-northwest Monday night.
It is forecast to gain additional strength and become a hurricane Tuesday.