The figure is far lower than the death tolls given by groups which have monitored the conflicts in the two countries.
"The coalition conducted 34,502 strikes between August 2014 and the end of April 2019," it said in a statement.
During this period, it "assesses at least 1,302 civilians have been unintentionally killed by coalition strikes."
The coalition said it was still assessing 111 additional claims of civilians deaths and was ready to receive new allegations or fresh evidence to review.
The coalition has repeatedly said it does all it can to avoid civilian deaths.
Amnesty International welcomed the latest acknowledgment of responsibility but said the real civilian death toll was likely much higher.
"The coalition remains deeply in denial about the devastating scale of the civilian casualties caused by their operations in both Iraq and Syria," said Donatella Rovera from the London-based group.
And while the coalition has admitted responsibility after cases were investigated by rights groups, it has failed to "provide reasons for the civilian casualties," she said.
"Without a clear examination of what went wrong in each case, lessons can never be learned," Rovera said.
In a report released last month, Amnesty and airstrike monitor Airwars found that coalition air strikes killed 1,600 civilians just in the four-months blitz to oust Daesh from the Syrian city of Raqqa.
Airwars, an NGO which monitors civilian casualties from air strikes worldwide, estimates more than 7,900 civilians have been killed in coalition raids -- well in excess of the total acknowledged by the coalition.
The Syrian Observatory for Human Rights, a Britain-based monitor, says coalition strikes have taken the lives of 3,800 civilians in Syria alone.
Daesh terrorists seized large swathes of Iraq and Syria in 2014, declaring a "caliphate" in areas they controlled.
But several offensives with coalition backing chipped away at the "caliphate" until it was declared eliminated on March 23.
Ambushes and hit-and-run attacks have continued in both countries.
The coalition is continuing to work "to deny Daesh any physical space and influence in the region as well as deny Daesh the resources they need to resurge", it said.