The Pentagon can advise the White House on a strategy for combating Islamic militants in the Middle East, but the buck stops with President Obama, Adm. Mike Mullen, former chairman of the Joint Chiefs of Staff, said Sunday.

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"There should not be any question, in the end, who decides this," Mullen said on NBC's "Meet the Press" program. "And that's the president."

The comments arrive as some in the Pentagon have left the door open to using ground troops in the fight against the Islamic State in Iraq and Syria (ISIS) even as Obama has taken that option off the table.

Gen. Martin Dempsey, the current chairman of the Joint Chiefs, told Senate lawmakers last week that he would recommend such a strategy if the situation on the ground evolved to require it – remarks that sparked a backlash among some on Capitol Hill who are vowing to oppose that route in any event.

"I think the generals should know that there's no appetite in the public for combat troops on the ground," House Minority Leader Nancy Pelosi (D-Calif.) said Thursday.

Mullen said Dempsey's comments have been "blown way out of proportion," arguing that Dempsey was simply trying "to explain, to some degree, how the process works."

"I don't know of any leaders, military or civilian, who are talking about brigade-sized units," Mullen said. "We certainly learned in these wars that it's important to have indigenous forces on the ground, and our ability to both train them and support them has made a difference."

Mullen named several Middle Eastern nations that can help in the fight, including Jordan and Bahrain, but suggested the ultimate success of the mission could hinge on the commitment of Saudi Arabia.

"The Saudis actually have a capable force," he said. "In the end, that becomes a question: Will the Saudis support us in that regard? And I don't know the answer to that question."