Updated

Kentucky Sen. Rand Paul and fellow Republican and former Vice President Dick Cheney widened their divide Sunday over U.S. involvement in Iraq -- the latest in their sharp, public disagreement over American foreign policy.

Paul, a potential 2016 presidential candidate, criticized those who supported the 2003 U.S. military invasion of Iraq and now blame the Obama administration for its handling of the aftermath, which includes Sunni Muslim militants having seized several towns and cities.

"What's going on now, I don't blame President Obama," Paul said on NBC’s “Meet the Press.” "But I do blame the Iraq War [for] the chaos that is in the Middle East.”

His comments are similar to recent ones he made on U.S. involvement in Syria and the Ukraine-Russia conflict and about those who consider the military option a first step in American foreign diplomacy.

Paul told CNN’s “State of the Union” that ousting Syrian President Bashar Assad could turn the country into a “Jihadist wonderland.”

“It’s now a Jihadist wonderland in Iraq precisely because we got over involved, not because we had too little involvement,” he continued.

Cheney, a strong supporter of going into Iraq during the George W. Bush administration to topple the regime of President Saddam Hussein, dismissed Paul as an "isolationist."

“He doesn't believe we ought to be involved in that part of the world,” Cheney said on ABC’s “This Week.” “I think it's absolutely essential."

Cheney says the U.S. needs to be realistic about the threat of Sunni insurgents in Iraq, citing a Rand Corp study that found the number of Jihadist terrorist groups has increased from North Africa to the Mideast.

"I think it's very important to emphasize that the problem we're faced with is a much broader one," he said. "We need an administration to recognize the fact that we've got this huge problem, quit peddling the notion that they got core Al Qaeda and therefore there's no problem out there."

Paul and Cheney laid out their respective arguments last week in separate Wall Street Journal op-ed pieces.

Paul argued that many of those now “clamoring for military action” are the same people who miscalculated the “cost, challenge and purpose” of the war in Iraq.

Cheney’s piece, with daughter Liz Cheney, criticized Obama, whom he also attacked Sunday for, like Paul, wanting the United States to have less of a Middle East presence.

"I don't intend any disrespect for the president, but I fundamentally disagree," he said Sunday. "I think he's dead wrong, I think we're in for big trouble in the years ahead because of his refusal to recognize reality and because of his continual emphasis on getting the U.S. to basically withdraw from [that part] of the world."

The Associated Press contributed to this report.