US military efforts against Islamic State have cost nearly $1bn so far and are likely to run between $2.4bn and $3.8bn per year if air and ground operations continue at the current pace, according to a think tank analysis.

But a ramp-up, including more air strikes and a significant boost in ground forces, could send costs soaring to between $13bn and $22bn annually, said the analysis released yesterday by the nonpartisan Center for Strategic and Budgetary Assessments.

“Future costs depend, to a great extent, on how long operations continue, the steady-state level of air operations, and whether additional ground forces are deployed beyond what is already planned,” said the report by Todd Harrison and other analysts.

Defence Secretary Chuck Hagel told reporters last week that the Pentagon has spent roughly $7mn to $10mn per day on operations against Islamic State since June 16, when it first deployed troops to assess the Iraqi military and advise its leaders.

The US began air strikes against Islamic State militants in Iraq on Aug. 8 and expanded them to Syria on Sept. 22. Coalition forces have carried out 290 air strikes in Iraq and Syria, of which the US military has conducted 265.

US planes are flying about 60 reconnaissance sorties per day, and some 1,600 US troops are being deployed in Iraq.

The think tank’s analysis estimated the cost of US operations against Islamic State through Sept. 24 at between $780mn and $930mn. That agreed roughly with Hagel’s estimate of the cost per day.

If air operations continue at a moderate level and deployed ground forces remain in the range of 2,000, then the cost of the US military effort against the militant Islamist group would likely run between $200mn and $320mn per month, the report said.

But increased air operations, coupled with the deployment of up to 5,000 ground troops, would cost between $350mn and $570mn per month. High-intensity air operations with a deployment of 25,000 troops could cost $1.1bn to $1.8bn per month, the report said.

Defence officials have indicated they will have to seek more funding because of the fight against Islamic State.

Army General Martin Dempsey, chairman of the Joint Chiefs of Staff, said last week that the Pentagon’s 2015 budget proposal assumed stable or declining commitments abroad and some flexibility to adjust military pay and healthcare and to retire weapons systems.

“Commitments have gone up,” Dempsey told reporters, noting that Congress has rejected some proposals to retire weapons and adjust military compensation.

“So if you’re asking me do I assess right now ... that we’re going to have budget problems? Yes.”

The centre said its cost estimates were based on publicly available information about the types of aircraft and munitions being used, as well as expenditures in previous operations.