The legacy that President Barack Obama wanted of disengaging from war in the Middle East is looking more doubtful than ever as the Pentagon reveals it is spending about $9m (£5.8m) a day battling Isis as it also prepares to send more troops as “advisers” to Iraq.

Giving its first official figures for the cost of the campaign against Isis which began in Iraq last year before extending into Syria, the Pentagon said it has so far spent a total of $2.7bn, most of it on air strikes in both countries, though most of the operations have been in Iraqi skies.

The Pentagon said that the USAF had absorbed two-thirds of the total spending, or more than $1.8bn. Daily combat, reconnaissance and other flights eat up more than $5m a day, it said.

The White House last week confirmed that President Obama had approved sending the additional 450 advisors to Iraq, raising the number of US military personnel in the country to about 3,500. The new contingent of troops are to open a new base in eastern Anbar province.

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The base, in al-Taqaddum, could serve as a model for still more mini-bases for the US troops, which may lead to even more advisers being sent there. The possibility of a chain of “lily-pad” bases was raised by General Martin Dempsey, chairman of the joint chiefs of staff, during a trip to Italy. “You could see one in the corridor from Baghdad to Tikrit to Kirkuk to Mosul,” he said.

All the troops at the base in Anbar will, as advisers, operate under strict limits that will, for example, keep them from the front lines.

Anbar province is a significant choice because it is Sunni-controlled. Part of their mission, aides confirmed, will be to reach out to the Sunni community in hopes of easing their suspicions of the Shia-dominated central government.