The father, Christopher Maffei, 43, allegedly kidnapped his 3-year-old daughter and 2-year-old son from their mother's home Tuesday, CNN reported.
A rental car registered to Maffei was found Wednesday, parked at an Alameda marina from which a 44-foot yacht had been stolen, police said.
"An extensive air and ground search was conducted ... but the vessel was not located," San Francisco police said.
Police said they believe Maffei abducted the children and made off with them on the yacht, which is named "Unleashed," KPIX-TV, San Francisco, reported.
Maffei, who was last seen at 6 p.m. Wednesday, has said in the past that he would like to sail to Monterey or Mexico, police said.