Sen. Lindsey Graham and Senate Armed Services Committee Chairman Sen. John McCain arrive before a news conference on Capitol Hill in Washington, Jan. 13, 2015

U.S. senators John McCain and Lindsey Graham called Sunday for 100,000 foreign soldiers, most from Sunni regional states but also including Americans, to fight the Islamic State of Iraq and Syria (ISIS) in Syria.

Both McCain, the chair of the Senate Committee on Armed Services, and Graham, one of its members, sharply criticised current U.S. strategy as insufficient and unsuccessful in defeating the extremists.

That strategy has consisted of carrying out air strikes against ISIS in Iraq and Syria in support of local ground forces, which have also received weapons and training.

“I think 100,000 would be (the) total requirement,” McCain told journalists in Baghdad when asked about the size of the anti-IS force he and Graham were advocating for Syria.

“That would not be hard for Egypt; it would be hard for Saudis, it would be hard for some of the smaller countries,” but Turkey could also provide forces, McCain said.

Saudi Arabia is already involved in a war in Yemen, while Egypt is battling an insurgency and Turkey is more concerned with Kurdish rebels than ISIS.

The force would also include some 10,000 American soldiers “providing capability the Arabs don’t possess,” said Graham, adding: “When’s the last time an Arab army’s manoeuvered?”

The two senators also called for the number of American forces in Iraq to be increased to around 10,000.

That figure would include special forces to conduct “more of the raids you saw not long ago,” Graham said.

American special forces accompanied Kurdish troops on an operation in Iraq last month during which one U.S. soldier was killed.

“This is different than the last two wars,” said Graham, referring to the 14-year war in Afghanistan and the nearly nine-year conflict in Iraq, during which the group that became ISIS was founded.

“This time (it would) be a large regional army with a small Western component. The last two wars have been large Western components with a very small regional force,” he said.

But even if this force were formed and defeated ISIS, it would then have to occupy part of Syria, spelling another potentially lengthy deployment of American ground troops in the Middle East.

“In my construct, it’d be an international holding force, Sunni Arabs would be holding that part of Syria where they’re welcomed,” after it was cleared of ISIS, Graham said.

But “the bottom line is, the whole international community would have to be part of holding,” he said.

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