WASHINGTON -- Mitt Romney on Sunday said the United States must remain open to sending U.S. troops to battle the Islamic State, something President Barack Obama has repeatedly assured the public will not happen.

Speaking on CBS "Face the Nation," the former Republican presidential nominee criticized Obama’s Middle East policy, saying the United States should have kept “American troops standing by in Iraq,” and armed moderate rebel factions in Syria, “so they would able to keep something like ISIS from being formed.”

Romney's comments followed the release of a video early Sunday that appears to show a third American citizen who was executed by the militant group. The victim is believed to be aid worker Abdul-Rahman Kassig, who was kidnapped by the Islamic State, also called ISIS, in October of 2013.

The United States is part of a coalition of nations conducting airstrikes against Islamic State targets in Iraq, but Obama has said repeatedly that American troops will not be sent to Iraq to fight the group. Romney said that by making his intentions clear about troops, Obama had weakened America’s influence in the battle against the Islamic State.

"When the president says that ISIS is a cancer and it must be eliminated, he's right,” said Romney. “But you don't say, ‘We're only going to use the following tools in doing so.’ You say, ‘We're going to do whatever it takes.’ If it takes our own troops, [Obama shouldn’t] take that source of our strength away from the battlefield.”

The majority of Americans oppose sending U.S. troops to Iraq for combat missions, according to one recent poll. Another survey of U.S. troops found that an overwhelming majority, 70 percent, oppose deploying the U.S. military to support Iraqi soldiers in the fight.