Fighting broke out between troops and ethnic minority rebels in the Chinese-speaking Kokang border region in northeastern Shan State this month when insurgents dressed in police uniforms launched a surprise raid on security forces.
Thousands of people have since fled to China to escape the ensuing gun battles, artillery strikes and fires, leaving Laukkai deserted.
Military sources said 28 civilians and police have been killed, while the commander in chief's office has reported at least 46 insurgents have also died.
Three more rebels were killed today during an army offensive in which "some military officers and other (lower) rank soldiers were killed and injured," it added.
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A military source who asked not to be named said the figures were in addition to 26 rebels the government said had been killed in a statement on March 6.
State media reported yesterday that "dozens of soldiers" had also been killed in the escalating clashes.
The bloodshed has threatened to derail de facto leader Suu Kyi's efforts to seal a peace deal with Myanmar's ethnic minorities, some of which have been fighting the state for decades.
A second round of peace talks initially scheduled for late February have now been pushed back to May.
This month's clashes in the Kokang region have also raised tensions with Beijing, which fears the deadly unrest will spill across its borders as it did in 2015.
The people of Kokang have strong bonds with Myanmar's giant neighbour -- locals speak a Chinese dialect and the yuan is the common currency.
Last week China called for an immediate ceasefire and this week officials have reportedly been holding talks with rebel groups in a bid to calm the fighting.