WASHINGTON (CNN) -

One U.S. lawmaker firmly believes the United States should keep its sons and daughters out of Iraq's increasingly tangled and bloody conflict.

"I'm not willing to send my son into that mess," Sen. Rand Paul, R-Kentucky, told CNN chief political correspondent Candy Crowley on Sunday.

Appearing on "State of the Union," Paul acknowledged that while the chaos in Iraq intensifies by the day, he believes advances by jihadist Sunni militants on Prime Minister Nuri al-Maliki's Shiite government forces do not pose an immediate threat to U.S. national security. Though he refused to rule out some kind of U.S. assistance, Paul said absent that threat, President Barack Obama's administration should not send ground troops to assist al-Maliki's government.

"Let's not be involved in the Iraq civil war," Paul said.

He painted the current security situation as a battle between a "feckless" ally in al-Maliki and "allies of al Qaeda" -- the Islamic State in Syria and Iraq, an al Qaeda splinter group. Paul said he doubted the jihadist fighters would contemplate action against the United States in the middle of their campaign to take Baghdad.

"I don't believe that ISIS, right now, is in the middle of a battle saying, 'Hmm, I think we're going to send intercontinental ballistic missiles to America,'" he told Crowley.

In an interview Friday with CNN's Kate Bolduan, Obama pressed Iraqi leaders to find a political solution to governing their nation. But as 300 U.S. military advisers head to the war-torn nation, Republican critics like Paul are laying the blame for the current crisis at the feet of the Obama administration.

"I think there's chaos in the Middle East, and the chaos is because we've created a vacuum," Paul said. "One of the reasons why ISIS has been emboldened is because we've been arming their allies."

While the Obama administration has reportedly dispatched weapons and other military assistance to moderate opponents of President Bashar al-Assad's government in Syria, details remain murky about just where those resources may have ended up.

Paul says some Sunni militants who were among the Syrian rebels, more radicalized than the administration anticipated, are now blitzing Iraq's major cities with U.S. weaponry.

"It's now a jihadist wonderland in Iraq precisely because we got overinvolved -- not because we had too little involvement," Paul said.

"We are where we are because we armed the Syrian rebels. We have been fighting alongside al Qaeda," he added.

He said any further action in Iraq should be put to a vote in Congress.