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In its 50-year history, Costco has never seen such demand for gas.
Earlier, Trump said he read a draft of an Iran peace deal.
Newsom's office cited an analysis that found that Chevron averaged more than 60 to 80 cents per gallon above unbranded alternatives.
Finding a gas station in the Bay Area has become more difficult in recent years as many stations have closed, driven in part by the high costs of removing potentially dangerous underground storage tanks and complying with state law.
"For Iran, the Clock is Ticking," Trump said.