Airwars -- a London-based collective of journalists and researchers that uses social media, eyewitness reports and other sources to compile its data -- said the concurrent assaults on Raqa in Syria and Mosul in Iraq were often "devastating."
The number is completely at odds with that of the US military, which so far has acknowledged the accidental deaths of 603 civilians since anti-IS operations began in late 2014.
Airwars director Chris Woods said the increased tempo of strikes in Mosul and Raqa accounted for some of the increase, but suggested the Pentagon's goal of "annihilation" of the jihadists had placed civilians at greater risk of harm.
Airwars said it assessed that between 529 and 744 non- combatants were killed in June, more than 50 per cent above the prior month's tally.
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Amnesty International yesterday called for a commission to investigate crimes against civilians in Mosul by all sides in the battle to liberate the Iraqi city from jihadists.
The charity said Iraqi and coalition forces had failed to take adequate measures to protect civilians.
"This is, I believe, the most precise campaign in the history of warfare," Townsend said.
"I would challenge the people from Amnesty International, or anyone else out there who makes these charges, to first research their facts and make sure they're speaking from a position of authority."
The US military's Central Command is currently wading through a backlog of old Airwars claims and so far has assessed most of these to be "non-credible.