China also vowed not to let the ethnic Chinese rebels operate from its territory, after the dramatic upsurge in conflict in Myanmar's northeastern state of Shan that has left dozens dead on both sides.
Urging both sides to "exercise restraint", Chinese foreign ministry spokeswoman Hua Chunying said in Beijing that more fighting "will have an impact on the stability of the China-Myanmar border areas and the security on the Chinese side of the border".
Myanmar authorities have blamed local Kokang rebel leader Phone Kya Shin for the fighting, and called on Beijing to rein in any local officials who might be helping the group on its side of the border.
Nearly 2,000 people have fled the area for central Myanmar, according to a report in state-backed media on today.
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Hua did not give details of the number of people who have crossed the border into China to escape the heavy fighting. The Myanmar military has launched airstrikes against rebels who tried to capture Kokang's main town of Laukkai.
Details of the fighting in the remote mountainous region remain difficult to confirm.
In 2009 more than 30,000 people flooded over the border into China as Myanmar's army launched an offensive against Kokang rebels.
The fighting earned Myanmar's then-junta a rare rebuke from China, the country's powerful northern neighbour which at the time was almost its sole ally on the international stage.
Myanmar's military last week said 47 of its own soldiers had been killed and dozens more injured in the first few days of the conflict, in unusually candid reports of casualty numbers.