Kachin Independence Army (KIA).
Shan state, which borders Thailand, Laos and China, is rich in resources and the site of three hydroelectric dam projects.
The latest attacks come as villagers in the area prepare for the rice harvest.
Many are stealthily returning home to collect their belongings and tend to their rice paddies, but the situation remains unstable, the Shan groups say.
US Assistant Secretary of State Daniel Russel, after talks this week with Myanmar armed forces chief Min Aung Hlaing, described the military operations and fighting in Shan and neighbouring Kachin state as "very worrisome". "We have concerns about the humanitarian crisis that is generated by the fighting.
We also have concerns that the fighting could set back the effort to build out a nationwide ceasefire to include non signatories," Russel told Reuters in Yangon.
"While there are two sides to the conflict, I urged the Burmese military to exercise restraint and to work in an effort to promote reconciliation and peace.
"The United Nations is also concerned about the fighting and reported up to 6,000 displaced people seeking refuge in monasteries and temporary shelters, said Pierre Peron, spokesman for the UN Office for the Coordination of Humanitarian Affairs (OCHA).
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