The Kenya Red Cross said it was sending humanitarian supplies to families who fled into Kenya after fighting erupted in the Ethiopian border town of Moyale this week and that its response would initially reach 1 000 households.

Hundreds of Ethiopians, mainly women, children and young people, crossed into Kenya after the fighting began on Wednesday, the Kenya Red Cross and local government officials have said.

Gunfire could still be heard on the Ethiopian side of the border on Thursday, according to local residents.

Kenya's Moyale town, which sits opposite an Ethiopian settlement of the same name, remained calm, but police were on high alert after reporting several incidents involving stray bullets.

The Kenya Red Cross said it had begun setting up a temporary shelter and distributing tents, blankets, sleeping mats, jerrycans, kitchen sets and fortified porridge flour.

"Many have arrived with very few belongings and urgently need shelter, food, water and health care," the organisation said in a statement late on Thursday.

A police report seen by Reuters said a stray bullet had lodged in the neck of a local woman in Kenya's Moyale town. She was admitted to a private hospital where the bullet was removed and is now in a stable condition, the report said.

Later on Friday, local government officials on the Kenyan side will meet to coordinate humanitarian assistance to displaced households.