Myanmar has been in turmoil since the military ousted civilian leader Aung San Suu Kyi from power in a February 1 coup, triggering a mass uprising that has seen security forces mount deadly crackdowns against protesters.

The anti-coup movement has garnered broad support across the country, including among some of the country's armed insurgent groups which have for decades been fighting Myanmar's military for more autonomy.

An estimated one-third of Myanmar's territory -- mostly in its border regions -- is controlled by a myriad of rebel groups, who have their own militias.

Since the coup, the Karen National Union (KNU) -- one of the largest armed groups in the country -- has seen hundreds of people flee to its territory in southeastern Karen state near the Thai border, an official with the group said.

"We think it could increase to between 6,000 and 7,000 people by the end of April," the KNU's general secretary Saw Tah Doh Moo told AFP.

He added that so far people fleeing anti-coup unrest had been activists, protesters and MPs with Suu Kyi's National League for Democracy party.

"Those who are now sheltering are more at the leaders' level, but if they (the military) keep pressing... it could be the broader population," he said.

The KNU has already seen fresh clashes with the military in its territory since the coup.

Besides people fleeing unrest in the cities, KNU territory currently has 5,000 Karen people displaced from local fighting that has been ongoing since December.

"It's our position, from our humanitarian point of view, that we have to give some shelter to these people who are in our area," he said.

Authorities in neighbouring Thailand's Tak province say they are preparing for a potential influx of refugees from Myanmar, and can support between 30,000 and 50,000 people.

About 90,000 refugees from Myanmar have lived in limbo on the Thai side of the border for many years after fleeing decades of civil war between the military and ethnic armed groups.

But Saw Tah Doh Moo said he thinks a further exodus to Thailand is unlikely.

"It's different because the people are more committed to (fighting) the coup," he said.