Israel will respond "quite forcefully" to Iran's Tuesday missile assault, potentially going after the country's nuclear facilities and going after Iranian Supreme Leader Ali Khamenei himself, retired U.S. Army Lt. Gen. Keith Kellogg, a national security adviser under former President Donald Trump and Vice President Mike Pence, said Tuesday.

Israeli Prime Minister Benjamin Netanyahu has told the world that he "'we have given you repeated opportunities to bring this thing to a conclusion,'" and as that hasn't happened, "I think he's going for the killing," Kellogg told Fox News.

"He's going to respond quite forcefully," Kellogg said. "I think if I was Iran I would say I think he's going to make a key shot at the nuclear facilities and going after the supreme leader."

Tuesday's air attack, he added, will set "everything in motion for a much wider war in the Middle East," as the Israelis have decided that they've had enough.

"It's probably about time," said Kellogg. This needs to be brought to some type of conclusion. If we are not going to help them conclude it, they are going to have to do it on their own. That's probably what they are trying to do."

Iran, by launching what could be as many as 250 missiles against Israel, has contributed to a situation that is "really spinning out of control," Kellogg said.

"You're starting to see a lot of missiles from Iran," he said. "They have got to the largest missile arsenal in the Middle East. You're looking at the defense system and they are trying to overwhelm the system."

The Aero 3 system and "David's Sling" are defending Israel, but the Israeli general policy is to make a "disproportionate response to an attack," Kellogg said.

"I think if you're looking at the Supreme Leader Khamenei, he's a risk," he continued. "I think the Israelis are going to come back hard at him and they should. This is going to escalate more and more. This is not for slowing down."

And the United States should remain "full square" behind Israel, no matter what it decides, Kellogg said.

"They are fighting our fight in the Middle East and we should acknowledge that and know that, and be on their side 100%," he insisted.

Meanwhile, Iran could be preparing yet another wave of attack, said Kellogg.

"When they hit at us at Al-Assad Air Base, in a situation with President Trump, we knew the attack was coming," he said. "It basically sat there for five or six minutes and said, OK we are done. He didn't kill anybody."

But the Israelis "do not respond like that," said Kellogg.

"They look at the threat much differently than we looked at the threat because we were separated and so far away," he said. "They look at it as a regional threat… they have proven they can go after the nuclear sites. This will be one of those times where I think they are saying okay, enough is enough, we are going to try to finish this. That's where you see the escalation."

And the Iranians "should be nervous," said Kellogg.

"When you look at the senior military commander in Israel, he has said repeatedly that we can reach out and touch anybody," he said. "The question is about what we call suppression of enemy air defense… Can they do it? I think they can. This is not going to end. They are not going to say game over. They shot 200 missiles. We're going to take our ball and go home."

And Netanyahu has a "great war cabinet," said Kellogg.

"Look at his generals in charge," he said. "You look at his minister of defense, it's a very tight-knit circle. They are all very aggressive in how they approach the world."

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