Thursday evening's airstrike that killed Iranian Gen. Qassem Soleimani -- the head of the Islamic Revolutionary Guard Corps' elite Quds Force -- was the "best way" for the U.S. to counter Iranian aggression, former CIA Station Chief Daniel Hoffman said Friday.

Appearing on "Fox & Friends" with hosts Steve Doocy, Ainsley Earhardt, and Brian Kilmeade, Hoffman said that although the U.S. has "a full range" of choices on defending itself from and responding to Iran, America needs to stay on its toes.

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President of Iran Hassan Rouhani praised Soleimani early Friday morning and promised via Twitter to "take revenge for this heinous crime" carried out by the United States.

Soleimani -- Iran’s top “shadow commander” -- was responsible for the deaths of hundreds of American and coalition service members and the wounding of thousands more, the State Department said.

The U.S. State Department issued a security alert Friday morning urging all U.S. citizens to “depart Iraq immediately” due to heightened tensions in the region.

"We need to be very alert," warned Hoffman. "I'm sure our state and local law enforcement is working with our intelligence community to be as alert as possible, collecting information and intelligence on potential Iranian threats."

"Make no mistake, when we counter Iran the way that we did, that's the best way to deter future attacks against us," he said.

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Hoffman said he thought U.S. strategy has been "pretty clear."

In April of 2019, Secretary of State Mike Pompeo told "Special Report" host Bret Baier than Soleimani was viewed in equal standings with the head of ISIS.

"Yeah, he's a terrorist," said Pompeo. "Qassem Soleimani has the blood of Americans on his hands."

"If you listen to Secretary of State Pompeo -- last month he said we would mount decisive action against Iran and their proxies in the event that our people and our installations were put at risk. So, the president took that decision and put it into force last night," Hoffman noted. "I don't see how anyone could be super surprised about this, frankly."

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Hoffman said he thought there has been "a rush to judgment" about the decision to strike.

"The president and his team have not briefed the Congress," he told the "Friends" hosts. "I wish some of our elected leaders would just hold a little bit on their rhetorical fire -- leave politics at the water's edge for a moment."

"Let's wait to hear from the administration with more details about the strike and planning that went into it -- as well as our planning, now postmortem for Soleimani, how we are going to plan on dealing with Iran going forward." he cautioned.

Fox News' Danielle Wallace, Frank Miles, Lucas Tomlinson, John Roberts, Mike Arroyo, and The Associated Press contributed to this report.