US President Barack Obama came under fire Sunday from Republican lawmakers and others who warned that a debacle in Iraq will give Islamist extremists a staging area for "the next 9/11."

Senator Lindsey Graham, a proponent of US air strikes, also called for the resignation of Iraqi Prime Minister Nuri al-Maliki and direct US engagement with Iran on the crisis set off this week by a lightning offensive by the Islamic State of Iraq and the Levant (ISIL) jihadist group.

Fighters from the group routed the much larger Iraqi army, seizing the country's second largest city Mosul and sweeping through the Sunni heartland towards Baghdad.

The United States moved an aircraft carrier and two guided-missile warships into the Gulf on Saturday as Obama weighed his options.

Retired military officers questioned whether air strikes were a viable near-term option with no US forces on the ground to provide precise targeting data.

But they and a former US ambassador to Iraq, Ryan Crocker, stressed the urgent need for high-level US diplomacy to drive Shiites, Sunnis and Kurds toward a political solution.

"I would support very carefully targeted air strikes, but they would have to be in conjunction with a serious, high-level, diplomatic effort that would engage the Shia, the Sunni and the Kurdish leadership," said Crocker.

"We have got to help the Iraqis come together in a unified fashion to confront a common threat."

Crocker, speaking on CNN's "Fareed Zakaria - GPS," warned: "The stakes are very high here.

This is Al-Qaeda 6.0. And if they consolidate their territorial gains, they will be in a stronger position than they ever were in Afghanistan prior to 9/11. And we know how that turned out."

Retired General Peter Chiarelli, a former commander in Iraq, said ISIL fighters "have an opportunity here, they have taken advantage of that opportunity, and I think we should really, really be concerned."

"I read someplace yesterday, where they're the richest terrorist group in the world after what they were able to seize in Mosul, so I'm concerned, and I think all Americans should be concerned," he told ABC's "This Week."

Graham, interviewed on CNN's "State of the Union," said Washington had to act "because Iraq and Syria combined are going to be the staging area for the next 9/11 if we don't do something about it."

"The people holding ground in Iraq also hold ground in Syria. Economic instability that comes from a collapsed Iraq will affect gas prices and our economic recovery," he said.

Another Republican lawmaker, House Homeland Security chairman Michael McCaul, stopped short of calling for US military action but pressed for an intensive diplomatic initiative with US allies in the region.

"They need us to lead them and we're not leading right now as a nation," he said on "This Week."

"This is the worst of the worst," he said of ISIL. "If they get back into the United States or western Europe, I see that as the biggest threat today."