Should Sen. Rand Paul run for president, he likely won't be able to count on support from former Vice President Dick Cheney.

In an interview Sunday on ABC's "This Week," Cheney said he will likely back a candidate who is more hawkish on foreign policy -- a stance at odds with Cheney's perception of Paul, a Kentucky Republican.

Cheney cautioned that he has not yet settled on a favorite potential presidential candidate. But, he added, "one of the things that's right at the top of my list is whether or not the individual we nominate believes in a strong America, believes in a situation where the United States is able to provide the leadership in the world, basically to maintain the peace, and to take on the al Qaeda types wherever they show up."

"Rand Paul, by my standards, as I look at his philosophy, is basically an isolationist," Cheney said. "That didn't work in the 1930s. It sure as heck won't work in the aftermath of 9/11, when 19 guys armed with airline tickets and box cutters came all the way from Afghanistan and killed 3,000 of our citizens."

Paul, meanwhile, in an interview on NBC's "Meet The Press," attempted to press the opposite point regarding Iraq - that he could support military intervention, but only with the support of the public and Congress.

"I'm not saying we never go to war, but if we're going to go to war there needs to be a vote of the American people through their representatives," Paul said.

But, earlier this week, Paul reiterated his broader national security stance, which indeed envisions minimal military intervention by the U.S.

Reagan spoke often of peace through strength,” Paul said this week at a conference sponsored by the socially conservative Faith and Freedom Coalition. “But I fear some in our nation, some in our party, have forgotten the first part of the sentence: That peace should be our goal even as we build our strength. Some in my party have distorted this ... into a misguided belief that we should project strength through war."

Cheney burst into the public discourse this week with a Wall Street Journal op-ed penned with his daughter Liz Cheney, which panned President Obama's foreign policy and national security performance.