As gas prices continue to soar in the U.S. and across the globe amid the war with Iran, Chevron executive Andy Walz suggested Americans could save money by driving less and trying to conserve energy. 

"People should try to drive less. They should try to conserve energy," Walz told CBS News when asked how Americans could try saving money at the pump. "We should be doing that all the time. Energy's essential for people's lives, but we should conserve it."

Since the start of the war at the end of February, ship traffic in the Strait of Hormuz, which carries roughly 20% of the world's oil and gas supply, has been greatly diminished. As a result, the price of Brent crude, the international benchmark, has spiked, hovering around $100 a barrel in recent weeks. 

Walz, Chevron's president of downstream, midstream and chemicals, said there's probably no "silver bullet" to help bring down prices for Americans over the long term while oil prices remain high for everyone else. 

"It's a global market for crude," Walz said. "We have crude here, that's closer to us, that we're all processing and using. That's helping Americans buffer their price. ... If this goes on for an extended period of time, it's probably gonna get tougher."

Walz also warned of possible supply chain issues if the crisis continues.

"America is more reliant on local production, but there's countries in Asia and other parts of the world that rely heavily on Middle East crude," he said. "They can't get it. They can't refine it. They can't make the products people need, and they're starting to run out. And that is a real problem. We're worried about price here. There's other countries that don't have the products. And to me, that is a big worry."

Watch more of Andy Walz's interview Wednesday on "CBS Mornings."