California Gov. Arnold Schwarzenegger seen on this June 12, 2008 file photo. (UPI Photo/Ken James)

The Republican governor said in a statement that offshore drilling was "not the answer" to higher fuel costs and urged a focus on non-petroleum energy.

"We will continue to foster a market for alternative energies because choice is the only way we will ultimately bring down fuel costs," Schwarzenegger said in a written statement.

President George Bush announced Monday he was lifting the executive order banning oil exploration in the U.S. outer continental shelf. Exploration remains blocked by a congressional ban that is likely to be renewed when it expires at the end of September.

The president and other Republicans have urged expanding offshore production beyond the Gulf of Mexico and Alaska as a means of increasing the supply of domestic crude.

Sen. Lisa Murkowski, R-Alaska, a leading proponent of offshore drilling, said in a written statement that the decision should be up to individual states.

A state opt-in process with revenue sharing is an equitable way to help the nation acquire more energy, while still giving states control over development off their coastlines," she said.