"We don't need to go to war. And we have to make that very clear to our Israeli friends," he said in an interview with CNN on Friday.
"We're not going to go to war. They're [Israelis] not going to go to war by flying over our airspace over Iraq. We're not going to support them," Brzezinksi added.
The political analyst also pointed to the repercussions of such an attack for the United States and the Middle East in general.
"If they [Israelis] do it, they will be on their own. The consequences will be theirs, because the price we'll all pay, based on a massive war, which the Iranians interpret as being done with our connivance, will be disastrous for us in Afghanistan, in Iraq, in the terms of oil, but also in the Middle East more generally," Brzezinksi explained.
The US and Israel have intensified the anti-Iran war rhetoric during the past weeks to put more pressure on Tehran to stop its peaceful nuclear energy program.
The war threats came after the Washington-backed sanctions against Iran failed to stop the country.
The US and Israel have repeatedly threatened Tehran with the "option" of a military strike, saying Iran's nuclear program may include a covert military aspect, a claim strongly rejected by Tehran.
Meanwhile, the International Atomic Energy Agency (IAEA) has never found any evidence indicating that Tehran's civilian nuclear program has been diverted towards nuclear weapons production.
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