Former Director of National Intelligence James Clapper warned that Israel's strikes in Iran have rocketed the two countries into an elevated level of tension, and that an escalation in fighting will be "harder and harder to control."

Clapper, who served in his post in President Barack Obama's White House, told CNN Thursday evening that the assumption was Iran and Israel are "attacking each other in the hopes of messaging each other, and that somehow these attacks are circumscribed and limited to convey a message."

But, he added: "I think we're rapidly growing out of that phase, and that the escalation ladder is going to get harder and harder to control, and that the messaging phase is perhaps over."

Clapper said he takes Iranian officials, "notably the foreign minister, at their word, and I don't think they're going to respond in kind, but they're going to respond with a larger attack that in their minds would be more effective than the first one."

Israel carried out an attack overnight inside Iran, near a military base and nuclear installation in the city of Isfahan, days after the Islamic Regime fired a barrage of more than 300 missiles and drones against Israel.

Iran was responding then to an Israeli strike in Syria that killed top leaders of its elite Iran Revolutionary Guard Corps earlier this month.

Clapper said the "tit-for-tat" attacks by the longtime Middle Eastern foes are at a "pretty serious turning point."

"I had commented earlier that ... it looks like the Iranians crossed the Rubicon by attacking, or attempting to attack, Israel proper. Well, the other side of that Rubicon appears now has been crossed by Israel. So, you know, where do we go from here?" he asked.