A 38-year-old man has been arrested after jumping into Lake Burley Griffin following a police pursuit from NSW on Tuesday morning.

ACT police were alerted to the pursuit by NSW police involving a black Ford Ranger after the driver crossed the border on Canberra Avenue in Fyshwick.

Police say the vehicle, which was towing a car trailer with a Toyota Hilux on it, crossed on to the opposite side of the road multiple times and drove on footpaths along the Lake Burley Griffin foreshore.

The vehicle stopped behind the National Gallery where the driver jumped into the lake.

Police escorted him back to shore and arrested him. He was subjected to a roadside drug test which returned a positive result for a prescribed drug.

A 35-year-old male passenger of the Ford Ranger is assisting police. A search of the vehicle uncovered ammunition and a knife.