WASHINGTON (CNN) -

It's a "very real possibility" that individuals with the extremist group ISIS may have crossed into the United States at the southern border, Texas Gov. Rick Perry said Thursday, though he added he doesn't have any evidence.

Because the border is insecure, Perry said that "individuals from ISIS or other terrorist states could be" taking advantage of the situation. "I think it's a very real possibility that they may have already used that," he told an audience at the Heritage Foundation in Washington.

"We have no clear evidence of that," he continued.

Perry said Texas has seen historic levels of individuals from countries with terrorist ties recently, including three Ukrainians arrested on a ranch in West Texas in the past two months, he said.

Perry used the argument to frame the broken border situation as a matter of national security.

"We need to have clear and compelling forces, both law and enforcement and otherwise, to send the message that the border is secure," the potential 2016 Republican presidential candidate said.

ISIS, a Sunni Muslim extremist group that refers to itself as the Islamic State, has waged a rapid campaign across Iraq this summer seizing towns and villages and targeting Christians, minority sects, and Shia Muslims.

In his remarks, Perry called for a more robust response to ISIS in Iraq, saying the Obama administration's recent actions have been inadequate.

"When they talk about limited airstrikes, they place a great emphasis on the word 'limited,' yet clearly more airstrikes are necessary," he said. "Nothing less than a sustained air campaign to degrade and destroy ISIS forces is required."

Asked by a reporter in the audience if he would support combat troops on the ground, Perry said, "all your options have to be open."