Tasmanian police are investigating reports that a man tried to lure a six-year-old girl into bushland, south of Hobart.

Police say the child was walking with her mother on the White Water walking track at Kingston yesterday.

They say the man did not grab the child, but he is believed to have spoken and used a hand gesture to suggest she move towards the bushes.

Acting Sergeant Jon Remess says there is no need for alarm, but is urging locals to be vigilant on bush tracks.

"I'd like to put out a public safety message and some reassurance that this is an isolated incident, we take all reports seriously," he said.

"If we can just get the message across to parents or any person who may be walking on these tracks around the Kingston area to be vigilant, walk with somebody, don't walk alone, stick to designated tracks and keep a mobile phone with you at all times."