Newsom's $11-billion proposal is designed to offset the rising prices consumers are paying at the pump and also includes savings for those who rely on public transportation. The plan would include $750 million in grants for free or substantially reduced public transit fare, but Californians who don't own a registered vehicle would otherwise not receive a refund.

The governor, who is up for reelection this year, would cap payments at $800 for any person with more than one vehicle registered under the person's name, though households with multiple vehicles registered to different family members could receive far more than that amount.

Newsom said the state is "taking immediate action to get money directly into the pockets of Californians who are facing higher gas prices."

Average gas prices in California are currently $5.875 per gallon, an increase of more than $1 from one month ago and $2 from one year ago, according to the American Automobile Assn.