Gabriel, 10, and Evan, 5, were "safe and sound" and Ruelas was taken into custody, he said.
He did not immediately have other details and said it was unclear when the family would be returned to California.
Ixtapa is about 190 miles southwest of Mexico City.
A statewide Amber Alert had been issued for Ruelas' minivan.
Ruelas and her children were last seen at around 3 p.m. Thursday at their Altadena home. Sheriff's officials said Ruelas left behind a note expressing plans to kill her children and then commit suicide.
Ruelas' husband died about 18 months ago and she could be depressed said sheriff's Lt. Greg Sisneros.
He said authorities began searching for the family after friends found the home empty and the note inside.
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