Government troops found 18 bodies, and captured eight wounded rebels who died in hospital Sunday night, according to state-run The Mirror newspaper.
Nearly 50 soldiers were killed and dozens injured in combat last week in the northern Shan state.
The army launched an operation Monday after rebels from the Myanmar National Democratic Alliance Army (MNDAA) of Kokang province seized eight weapons from a local militia, the Global New Light of Myanmar reported.
Other ethnic rebel groups including the Kachin Independence Army, the Ta'ang National Liberation Army, the Arakan Army and Shan State Army-North in the Shan state joined them to fight government troops, Kokang rebel spokesman Htun Myat Linn said.
The army was using helicopter gunships and fighter jets to attack rebel positions in Laukkai township in Shan state since Tuesday, media reports said.
"We are now leaving the town as it seems government troops would heavily attack the rebels who are holding some areas of the town after all people were moved to Lashio," local businessman Min Min said.
"Some rebels are in the town and using snipers in fighting in some area of the town," he said.
Thousands of people in the region have crossed the border into China to escape the fighting.