The former commander of U.S. Central Command warned Sunday that American forces were "vulnerable" to an attack by Iran or its proxies, one day after the unprecedented Iranian missile and drone barrage against Israel.

"Our forces distributed across Iraq and Syria, supporting the Armed Forces of Iraq and anti-ISIS operations and supporting our SDF [Syrian Democratic Forces] partners in eastern Syria—those forces are vulnerable to an Iranian or an Iranian proxy attack," retired Marine Corps Gen. Frank McKenzie said on CBS' "Face the Nation."

"We recognize that. I think that's why the president's been very forceful in warning them."

But McKenzie also called it "very instructive" that Iran "did not choose to attack us as they conducted a major strategic attack on Israel."

"The Iranians know that we have the capability, if they choose to fight us, to hurt them very badly. And I think that the Iranians will think long and hard before undertaking attacks against us in the future," he said.

Iran launched Saturday's attack on Israel in response to suspected Israeli airstrikes on the Iranian embassy compound in Syria that killed two generals on April 1.

Israel has neither confirmed nor denied responsibility.

McKenzie led Central Command from March 2019 to April 2022, commanding U.S. military operations from northeast Africa across the Middle East to central and south Asia.

Central Command's top priority is deterring Iran, followed by countering violent extremist organizations, according to its website.

On Sunday, he said his only "strategic advice" to Israel regarding a potential response was that "you want be narrow" in terms of its targets, of which he said "the Israelis have a lot to choose from, both inside Iran and outside Iran."

"You want to make sure that it has a definable beginning and a definable end, and the Iranians know when it's over. But the fact of the matter is, Israel can name its price right now. And that's a very heady position to be," he said.

"But it's also a position that calls for exercise of strategic restraint, and a view to the long term. And Israel has an opportunity here, I think, to demonstrate that, and to seize the diplomatic initiative, really, in an arena where they struggled to do it over the past few months."