The cost of the US-led war against the Islamic State (Isis) militant group has totalled at least $780m, according to a new estimate, as US drones and warplanes continued to attack Isis positions in Iraq and Syria on Monday.

The US defense secretary, Chuck Hagel, said on Friday that the US military is spending up to $10m a day and is likely to request more money from Congress to fund a war whose duration is uncertain. In August, before the US expanded strikes against Isis into Syria, the Pentagon estimated its daily war costs at $7.5m and has yet to provide a more precise estimate.

The Center on Strategic and Budgetary Assessments (CSBA), a thinktank influential with the Pentagon, estimated on Monday that the air war has already cost between $780m and $930m between 8 August, when it began, and 24 September.

Congress has not voted on going to war, outside of authorizing the military to train a proxy Syrian rebel ground force, and will not do so until after the November midterm elections at earliest.

The CSBA priced out estimates running a gamut of options proposed by politicians, retired military officers and pundits for escalating the war. What it called a “moderate level of air operations”, involving 2,000 “deployed ground forces” – a level slightly higher than the 1,600 ostensibly non-combat security and “advisory” US forces in Iraq now – would total as much as $320m each month and $3.8bn annually.

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