Police are searching for a cyclist in Canberra who mowed down four school children while they were running a cross-country event.

The children were running near a waterway construction area in Mawson when the man began swerving at them and swearing.

Officers say the man then rammed his bike into one of the children, injuring them, and then came off his bike in the process.

He then re-mounted and targeted three more children, knocking each of them down and running over one boy's foot.

The attack happened on the morning of Friday, April 13, but police have only now made their search public.

According to witnesses, the man was white and seemed to be in his late twenties, with a light beard and a deep voice.

He was wearing shorts, a grey singlet and cap, and the children described his clothes as tattered and torn.

Police said he was riding a maroon mountain bike, and have called for witnesses to come forward.