Troops had been involved in at least 13 clashes with rebels, a newspaper said
The BBC's Myanmar correspondent, Jonah Fisher, says it is the heaviest fighting in at least two years.
It comes as the government tries to sign a peace deal with rebel groups.
There are reports that thousands of people have been leaving the area to escape the fighting.
China said on Tuesday that some people had crossed over into its southern Yunnan province, and that they were being looked after.
The Kokang are a Han Chinese ethnic group, and their armed wing a remnant of the Burmese Communist Party which fragmented in 1989.
For years they have run a largely autonomous strip of land on Myanmar's north-eastern border with China.
This dramatic upsurge in fighting appears to have been triggered by the return of one of their leaders - Phone Kya Shin - from five years of exile in China.
In 2009, Phone Kya Shin was forced to flee by Burmese troops - but he has now returned promising to restore the rights of the Kokang people.
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