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Destroying the so-called Islamic State is going to require a renewed U.S. ground troop commitment in the Mideast, Republican presidential candidate Lindsey Graham said Wednesday. Anything but the total eradication of the terrorist group could result in attacks in the United States, he added.

Following last week's attacks in Paris, Graham released a plan he said would eliminate ISIS, or ISIL as it's also referred to, and stop "the rise of radical Islamic extremism."

Describing his plan on CNBC's "Squawk Box," the senator from South Carolina said Wednesday he'd organize a large regional force in the Mideast to lead the fight against ISIS, and then have Western powers, including the U.S., just support the effort — kind of the opposite of what happened when the U.S. and its allies invaded Iraq and Afghanistan.

"Egypt, Jordan, Saudi Arabia and Turkey would be the center of gravity of this [regional] force," he said. The regional force would be supported by U.S. ground troops, he said. His plan says to "send a force of 10,000 troops to Iraq to reestablish stability, take back lost territory, and destroy radical extremist groups like ISIL."

Graham, who serves on the armed services committee, said the regional powers in the Mideast are now more willing to fight against ISIS because they perceive the group as a greater threat than even the late Saddam Hussein was when he led Iraq. "No one ever believed Saddam Hussein would come into Jordan or Egypt and take over," Graham argued. "The region believes ISIL would cut their head off."

As for Russian and Iranian involvement, Graham said, "Under no circumstance would I work with [Vladimir Putin] and the Iranians regarding Syria if the price to fight ISIL was to keep [Bashar Assad] in power."

"If they want to help us fight ISIL without keeping Assad in power, that's a good deal," he said. Russia is currently engaging in airstrikes against ISIS and other rebel groups in Syria, which is an ally of Moscow.

Using a World War II analogy, Graham said, "ISIL is Germany. Assad is Japan. If you don't fight Syria, Lebanon and Jordan are going to fall ... you can never fix Iraq ... [and] they're going to hit us here at home."

If ISIS is not neutralized, it's almost "100 percent certain" the United States will get attacked, he warned.

Concerning the debate over whether the U.S. should let Syrian refugees into the country, Graham said, "I'm not saying never. But based on Paris, we should have a time out ... until we find a vetting process."

"But here's what I want to let Republicans know: If you stop the refugee flow, you have not protected the homeland. ... There are 20 different ways to get to America," he said. "There's no substitute for destroying ISIL in Syria and Iraq."

The senator said the destruction of the Islamic State cannot be achieved from airstrikes alone, stressing the importance of adding a ground troop component as he previously described; "the sooner the better."