More than 1,100 civilians have been killed in the country's bloody crackdown on dissent and more than 8,000 arrested since the coup, according to a local monitoring group.
The fighting broke out when more than 100 troops arrived in four military vehicles to secure the area in Myin Thar and five other nearby villages.
The junta has previously said it would hold new elections within two years, but has also threatened to dissolve the NLD.
Coronavirus infections are rising sharply in Myanmar, with authorities reporting almost three thousand cases Monday, up from around 100 per day in early June.
On Tuesday, Min Aung Hlaing met with Russian Defence Minister Sergei Shoigu, who hailed strong military cooperation between the countries.
At least eight people were killed in the gun battle in Mandalay, the military-run Myawaddy Television's news service reported.
What should be New Delhi’s policy towards democratic struggles in neighbouring countries? Can we remain silent when institutions slowly face extinction?
One slogan painted on a bus stop said the military was being misused to protect junta chief Min Aung Hlaing, and urged soldiers not to shoot civilians.
The Karen National Union, the leading political body for the Karen, for now is shouldering all of the displaced people's basic needs for food, shelter and security.
Last week a junta spokesman said a now-detained chief minister had admitted to giving her $600,000 and more than 10 kilograms (22 pounds) of gold bars.
A man in Myanmar faces up to two years in jail after he was arrested for allegedly defaming the military in an interview he gave detailing his harrowing life as a child soldier.