Even as it provides support for Iraq's battle to retake Mosul, the U.S. led-coalition is laying the groundwork to push Islamic State militants out of the Syrian city of Raqqa, U.S. Defense Secretary Ash Carter said Tuesday.

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But a senior military official cautioned that conducting major operations in Raqqa and Mosul at the same time would stretch the coalition. He says the Raqqa campaign should wait until the Iraqis have made more significant progress in Mosul, where resistance from the militants has been described as heavy.

Mosul and Raqqa are the two main strongholds of the Islamic State group, acting as the capitals of their so-called caliphate and providing a source of revenue and territory. The Iraqi military, supported by U.S. and coalition air power and military advisers, began the push to retake Mosul on Oct. 16. The battle is expected to take months and follows successful campaigns this year to retake the main cities in Iraq's western Anbar province.

The senior military official said that if the Mosul and Raqqa operations were done now, the biggest strains would be on fighter jets and reconnaissance aircraft. The coalition should be able to start the Raqqa operation in the near future, the official said, but declined to give a more precise timeline.

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The official said that the U.S. does not anticipate the need for any additional U.S. forces in Syria right now. There are currently up to 300 U.S. special operations forces working with Syrian rebel forces.

The official was not authorized to discuss the Iraq or Syria operations publicly so spoke on condition of anonymity.

Carter, speaking at a news conference, said there has been no delay in the intended start of the Raqqa operation, and that there will be "overlap" with the Mosul fight. He said that has been the plan all along.

Carter also touted the military's success in Mosul, praising the Iraqi security forces and the Kurdish militia, known as the Peshmerga, for gains they have made in the march toward the city. Islamic State fighters have countered with suicide attacks, car bombs and other attacks. They are expected to give ground gradually on the outskirts of Mosul but then stiffen their resistance as the fighting moves closer to the center of the city.

"The collapse and destruction of ISIL in Iraq and Syria will destroy both the fact and the idea that there can be a caliphate based upon this ideology," Carter said, using another acronym for the Islamic State group. "However, there will continue to be, and there are now, those there or elsewhere who aspire to either coordinate or inspire attacks on our homeland."

Carter was speaking alongside French Defense Minister Jean-Yves Le Drian after a meeting with 11 other defense chiefs to discuss progress in the campaign to defeat the Islamic State group. The 13 countries at the Paris meeting Tuesday represent the largest military contributors to the counter-IS campaign. This is the fifth time the coalition has met, and another session is scheduled for later this year.

Carter also said that the Mosul operation has already achieved the reduction in the flow of foreign fighters to the Islamic State.

European leaders, including the French, have expressed worries that the battle to retake Raqqa hasn't begun yet, because of fears that IS leaders there will continue to plot and inspire attacks, like the ones like the ones that rocked France and Brussels in the past year.

Speaking to reporters, Le Drian said that taking Raqqa is a "strategic objective" and remains the focus of attention.

A key topic during the ministers' meeting was the risk that IS would plot or inspire more attacks against the U.S. and its European allies. And Le Drian said that even as the Islamic State's physical plan to create a caliphate collapses because of the military campaign, it remains a "virtual" threat by inspiring others to conduct violent attacks.