The refugees, mainly from the Somali border town of Bulo Hawa, are reportedly fleeing inter-factional fighting.
Armed clashes taking place appear to be over control of the road to Mogadishu.
Land mines have been laid on the road to Bulo Hawa, and the road between Bulo Hawa and Luuq, southern Somalia, has been closed, the statement said. At present, the refugees are staying with relatives and friends in Mandera. Some brought belongings by donkey-cart or on local transport, while others only managed to carry a few personal effects as they walked across the border. Although Kenya has maintained an open border policy in the area, the Kenyan local authorities have recommended that no refugee camp be established as it could encourage the spread of fighting across the border. They have also warned against the distribution of humanitarian assistance for the same reason.