Former vice president Dick Cheney and his daughter said Sen. Rand Paul's (R-Ky.) foreign policy views would make it difficult to support him as a presidential candidate. (Jackie Kucinich/The Washington Post)

Former vice president Dick Cheney sought Sunday to draw a sharp distinction between his position on Iraq and Sen. Rand Paul's, marking the latest fight over foreign policy in a Republican Party torn between military hawks and those who are far less keen on intervening abroad.

Appearing on a pair of Sunday morning news shows, Paul (Ky.) argued that turmoil in the Middle East is at least partly the result of U.S. involvement in Iraq and Syria. Cheney, a leading advocate of military action in Iraq during the presidency of George W. Bush, hit back sharply against Paul's warnings about too much U.S. military action overseas.

"If we spend our time debating what happened 11 or 12 years ago, we're going to miss the threat that is growing and that we do face. Rand Paul, with all due respect, is basically an isolationist. He doesn't believe we ought to be involved in that part of the world. I think it's absolutely essential," Cheney said on ABC's "This Week with George Stephanopoulos."

Paul said on CNN's "State of the Union" that "there's chaos in the Middle East, and I think the chaos is because we have created a vacuum. Before the Iraq war, I think there was somewhat of a standoff between Sunni and Shiite, had been for maybe 1,000 years off and on."

He also said that the Islamic State of Iraq and Syria, a militant group fighting the Iraqi government, have been "emboldened" because "we have been arming their allies. We have been allied with ISIS in Syria. They have had a safe haven because we have been arming the rebels to keep [Syrian President Bashar al-Assad] away from them."

Cheney acknowledged that "there are no good, easy answers in Iraq." But he argued for a more robust U.S. military presence in the region.

"What I would do now," he said, "is, among other things, be realistic about the nature of the threat. When we're arguing over 300 advisers when the request had been for 20,000 in order to do the job right, I'm not sure we've really addressed the problem. I would definitely be helping the resistance up in Syria, in ISIS's back yard, with training and weapons and so forth, in order to be able to do a more effective job on that end of the party."

Paul said the United States needs to first see what the Shiites in Iraq will do to defend themselves against militants before it decides whether to launch airstrikes.

"If the Shiites aren't willing to fight for their country, it may be that their country is not going to exist," he said.

Democratic and Republican lawmakers weighing in Sunday agreed that ISIS is or could become a threat to U.S. national security.

"I believe it can be. I believe that they're recruiting in Europe," Senate Intelligence Committee Chairman Dianne Feinstein (D-Calif.) said on "State of the Union."

Sen. Marco Rubio (R-Fla.) said on CBS's "Face the Nation" that, "Without a doubt, I think this is an urgent counterterrorism matter. I know a lot has been talked about the future of Iraq itself as a country, and that's a very legitimate issue that needs to be looked at, but for me this is not about nation-building, or imposing democracy — this is a counterterrorism risk that we need to nip in the bud. It is my view that we will either deal with ISIS now or we will deal with them later. And later they are going to be stronger and harder to reach."