BEIJING, China (CNN) -- Some of the tens of thousands of refugees who fled to China to escape fighting in Myanmar are beginning to return home as tensions have eased, police said.
Refugees from Myanmar sit with their possessions at a camp in Zhenkang, in southwest China, on Sunday.
An estimated 37,000 people were displaced by the fighting, Meng Sutie, police chief in southern China's Yunnan Province, told China's state-run Xinhua news agency Sunday.
The exodus of residents along the border grew to a flood last week as Myanmar government troops battled ethnic minority groups and their armies in the country's northeast. The region has an estimated population of 150,000.
There were casualties on both sides of the border, according to Meng. Shells fired into Chinese territory killed one person and injured two others, while fighting in Myanmar killed a Chinese and wounded 13 more.
In a rare criticism of Myanmar's ruling military junta, Chinese Foreign Ministry spokeswoman Jiang Yu said Friday that China hoped Myanmar could properly solve its domestic issues and safeguard the stability of its border with China, Xinhua reported.
China has been providing emergency shelter, food and medical care for the refugees.