Two senior U.S. senators called on Sunday for Washington to nearly triple military force levels in Iraq to 10,000 and send an equal number of troops to Syria as part of a multinational ground force to counter Islamic State in both countries.

Republicans John McCain and Lindsey Graham criticized President Barack Obama’s incremental Islamic State strategy, which relies on air strikes and modest support to local ground forces in Iraq and Syria, and said the need for greater U.S. involvement was underlined by this month’s Paris attacks.

“The only way you can destroy the caliphate is with a ground component,” said Graham who is seeking his party’s presidential nomination. “The aerial campaign is not turning the tide of battle.”

McCain, chairman of the Senate Armed Services Committee, recently proposed intervention in Syria by a European and Arab ground force backed by 10,000 U.S. military advisers and trainers.

On Sunday he and Graham told reporters during a visit to Baghdad that U.S. personnel could provide logistical and intelligence support to a proposed 100,000-strong force from Sunni Arab countries like Egypt, Turkey and Saudi Arabia.

Graham said special forces would also be included.

Obama last month ordered the deployment of dozens of special operations troops to northern Syria to advise opposition forces in their fight against Islamic State, adding to an increasingly volatile conflict in Syria.

Russia and Iran have ramped up their military support for President Bashar al-Assad’s fight against rebels in Syria’s four-and-a-half year civil war, while the Paris attacks showed how Islamic State has extended its reach to Western cities.

U.S. counter-terrorism experts have warned that deploying ground troops risks backfiring by feeding Islamic State’s apocalyptic narrative that it is defending Islam against an assault by the West and its authoritarian Arab allies.

The U.S.-led coalition which has been bombing Islamic State targets in Syria and Iraq for more than a year relies heavily on American resources despite including some 60 nations.

McCain said it would be possible but not easy to rally Arab allies to contribute to the proposed ground force in Syria.

“The question… is being asked all over the capitals of the West right now,” he said. “(Arab) countries for a long time have not seen what’s happening as a direct threat to them. Now I believe that they do.”

The senators said removing Assad, who is backed by Russia and Iran, was key to getting Arab Sunni states to back the proposed ground force.

IRAQ

In neighboring Iraq, where about 3,500 U.S. troops are currently advising and assisting Iraqi forces, Graham said an increased American presence would include forward air controllers and aviation assets as well as special forces to carry out raids like one last month which resulted in the first U.S. combat death in Iraq since 2011.

The senators met earlier with Iraqi Prime Minister Haider al-Abadi who they said had welcomed the idea of more U.S. troops.

“If you went up to 10,000, you’re not getting pushback from the Iraqis,” said Graham. “The difference between 3,500 and 10,000 is meaningless politically inside the country (but) militarily significant.”

However, government spokesman Saad Hadithi said Abadi had not requested U.S. combat troops on the ground but rather asked for more arms and advisers to increase air support for Iraqi forces. Hadithi declined to speculate about the number of additional personnel under discussion.

Leading Iraqi politicians have repeatedly voiced opposition to a greater role for U.S. forces, which withdrew in 2011 after a nearly nine-year war that left tens of thousands of Iraqis dead.

Iranian-backed Shi’ite Muslim militias seen as a critical bulwark in the fight against Islamic State have also resisted U.S. involvement.

“One reason I’d want to have more American troops is it neutralizes the Shia militia advantage to some extent,” said Graham.