Thousands of people have fled clashes between the Myanmar military and ethnic rebels along the border with China, a Chinese official said, as fighting threatened leader Aung San Suu Kyi's top goal of reaching peace with minorities.

About 30 people were killed on Monday in the attack staged by ethnic Chinese insurgents in the town of Laukkai, 800 km (500 miles) northeast of commercial hub Yangon, prompting thousands to seek refuge across the border in camps in China.

Suu Kyi's nearly one-year-old government is increasingly besieged by ethnic rebels, grappling with an alliance of militias in Myanmar's north and a new insurgency by Rohingyas rebelling against decades of persecution in the northwest.

"Thousands of people have crossed into China," said the Chinese government official, who declined to be identified because of the sensitivity of the issue.

Hotel workers in Nan San, a town abutting Myanmar's restive Kokang region where the fighting is taking place, described disoriented people moving rapidly into the town.

"There are so many people here and the traffic is chaotic. There are thousands of refugees here and they look frightened. Some of them brought suitcases with them, while some only brought some light clothes," said a staff member at the Golden Star hotel in Nan San who identified himself by his surname Li.

The 42-year-old owner of the Fuyuan Hotel, who identified himself by his surname Yang, said: "All we can do is to help them and give them food. Chinese people here are very worried about our safety."

Yang compared the scenes to those in 2015, when tens of thousands escaped fighting between the army and the predominantly ethnic Chinese Myanmar National Democratic Alliance Army (MNDAA) - the same group that attacked on Monday.

MNDAA is part of the Northern Alliance, a coalition of rebel groups comprising one of Myanmar's most powerful militias, the Kachin Independence Army, and two smaller groups that have been in a stand-off with Myanmar's military since clashes in Kokang two years ago.

On the Myanmar side of the border, some 300 people were waiting to be transferred to a camp for internally displaced people in the town of Chinshwehaw near Laukkai, said Saw Shwe Myint, an official from the Myanmar Red Cross in Laukkai.

"We are discussing with our partner organisations how to transfer these people to Chinshwehaw," he said. About 200 people were transferred on Tuesday.

Those in the camp comprised local residents and migrant workers from other parts of Myanmar, Saw Shwe Myint said. "I do not hear the fighting right now but I heard shooting this morning," he said.

China called for an immediate ceasefire between the two sides on Tuesday, urging them to resolve their differences through peaceful means.