Clashes broke out after rebels from the Myanmar Nationalities Democratic Alliance Army (MNDAA) attacked police and military posts in Laukkai town.
At least 30 people were killed on Monday after rebels launched a surprise attack on police and military posts in a Myanmar town bordering China, authorities said.
Artillery and small arms fire continued throughout the day in Laukkai, a main town in the Kokang region of the northeastern state of Shan.
Rebels from the Myanmar Nationalities Democratic Alliance Army (MNDAA) launched the attack early on Monday.
A separate group of fighters later attacked locations in the main town.
"According to initial information, many innocent civilians including a primary school teacher ... were killed because of attacks by the MNDAA armed group," the State Counsellor's Office said in a statement.
Some attackers wore local police uniforms, it said.
The clashes are some of the worst to break out in the Chinese-speaking Kokang region since fighting in 2015 left scores dead and forced tens of thousands to flee across the border into China.
Myanmar is already torn by various ethnic insurgencies. But the Kokang conflict has raised tensions with its giant neighbour.
Aung San Suu Kyi's government is desperate to end the decades-long borderland conflicts, but intensifying fighting threatens peace efforts.
An army source told AFP fighting was continuing as darkness fell.
"Residents in town are fleeing. We do not know exact figures yet," the officer said.
The Northern Alliance, an umbrella group of rebels including the MNDAA which has yet to join national peace talks, confirmed its members were fighting in Laukkai.
But in a Facebook post it said they carried out the attack "to resist an enemy offensive in self-defence" and cited Myanmar military operations since December.
The latest fighting raises the spectre of a fresh refugee exodus into China.
In early 2015, tens of thousands fled when dozens of civilians, rebels and army troops died in months of fighting across the remote and mountainous region.
China said Myanmar warplanes dropped bombs on its side of the border during that bout of fighting.
Kokang has strong bonds with China as local people speak a Chinese dialect and China's yuan is the common currency.
Skirmishes with the Northern Alliance have intensified across Shan state since late last year, claiming more than 160 lives across an arc of land in the long border region.