The NHC said, with maximum sustained winds of 120 miles per hour, Bud is now moving northwest at about seven miles per hour.
"A turn toward the north-northwest is expected on Tuesday, and this general motion should continue into mid-week".
Hurricane Bud, the second official hurricane in the eastern Pacific Ocean, upgraded to a Category 3 storm on Monday, June 11.
Some additional strengthening is possible today but a slow weakening should begin tomorrow.
In its latest update at 6am MDT, the NHC said up to 10 inches of rain could fall in isolated regions of southwestern Mexico on Tuesday afternoon. "These rains could cause life-threatening flash floods and mudslides", the agency warned.
At its peak, Aletta was a Category 4 hurricane when it was first detected about 500 miles off Mexico's west coast late last week and scared up heavy swells that swept across the west coast from Baja, California and led to strong rip current conditions.
The Mexican government discontinued the tropical storm watch for Manzanillo to Cabo Corrientes, the NHC said.
The center said the hurricane's core was moving farther from Mexico's southwestern coast but still could generate unsafe heavy surf and rip currents over the coming days.
The Atlantic hurricane season lasts until November 30.
The National Hurricane Center is monitoring an area of storms over the southwestern Caribbean Sea. The depression is now located about 665 miles southwest of the southern tip of Baja California with maximum sustained winds of 35 miles per hour.