Bush: Obama "has really weakened our hand" against the Islamic State. (AP Photo/Paul Sancya)

Jeb Bush said Wednesday that concerns he’d be accused of launching a “third Bush war” wouldn’t keep him from sending American troops overseas, and accused President Obama of policy failures that allowed the Islamic State to gain a foothold in Iraq.

“Well, had we kept the 10,000-troop commitment that was there for the president to negotiate and to agree with, we probably wouldn’t have ISIS right now,” the former Florida governor told conservative radio host Hugh Hewitt. “So to reflect on this...by putting all these preconditions, the president has really weakened our hand.”

And in response to a question about his fears of being tarred with a “third Bush war” -- a phrase he never used himself -- Bush said he "wouldn’t be conflicted by any legacy issues of my family.”

"I actually, Hugh, am quite comfortable being George Bush’s son and George Bush’s brother,” he said. “It’s something that gives me a lot of comfort on a personal level, and it certainly wouldn’t compel me to act one way or the other based on the strategies that we would be implementing and the conditions that our country would be facing.”

He added that the 2016 campaign wouldn't be won or lost on his political lineage and connections -- or on Hillary Rodham Clinton's.

“If the campaign’s about a dynasty, I’m not sure that that’s going to work,” he said. “If it’s about how you advance ideas that will help people rise up then it will be an inspiration for others, and that’s what we need to do.”