Kokang is a mostly ethnic Chinese region where rebels have observed a two-decade-old ceasefire with the government.
The rebels in a statement issued via the Myanmar Peace and Democracy Front, a newly formed alliance of four ethnic groups, said the army was pressuring its fighters to join a border security force under state control ahead of Myanmar's elections planned for 2010.
But the groups are reluctant to do so.
"We haven't had anything like this happen for about 10 years... Many people have been coming across the border"
Xie Feifei, shop owner in China's Nansan town
"Tensions between the junta and these cease-fire groups are extremely high and military confrontations between them are appearing frequently," they said in the statement which was issued by the US Campaign for Burma on their behalf.
"With anticipation of resurgence of war, tens of thousands of ethnic people have fled."
The US Campaign for Burma said the mobilisation of troops was a move by the military rulers to force ethnic groups to form political parties to contest next year's election, the first in Myanmar, formerly known as Burma, in 20 years.
The statement also said the military standoff was triggered after Myanmar troops tried to raid the home of a rebel leader, where illegal drugs were allegedly being produced.
On the Chinese side an official from the Zhenkang County Public Security Bureau surnamed Li confirmed the mass crossings but gave no details.
A local trader named Liu said the refugees had arrived in Nansan in distinct waves, and many had returned home after a few days.
He said some of his Myanmar business partners and friends have sold off their jewellery, mobile phones and other valuables to flee.
"Businesses have been badly affected," said Liu. "Many people from Burma usually cross the border to buy clothes and other things. ... Not many people are coming to shop now."
Liu said the local government has set up refugee camps, while some people have been moving further into China.
Xie Feifei, a shop owner in Nansan, said the refugees were being housed by the local government in disused or half-built homes.
|Myanmar's ruling generals are gearing up for next year's general election [EPA]
"We haven't had anything like this happen for about 10 years," Xie told Reuters by telephone on Wednesday.
"Many people have been coming across the border but it's fallen off now. I think everyone who wants to escape has already."
Earlier this month, Human Rights Watch called on Myanmar's military government to immediately end attacks against civilians after thousands were displaced in Shan state.
It said the army had reportedly deployed battalions to clear civilians from large areas in central Shan between July 27 and August 1, burning down more than 500 houses as they attacked 39 villages in the area.
Myanmar, which has been ruled by the military since a 1962 coup, is home to more than 100 different ethnic groups.