Councillor Maggie Taylor issued her appeal after a recent collision between a cyclist and pedestrian closed the bridge for half an hour.
She said: “The Tay Road Bridge central walkway is a great resource for people to be able to get out in the fresh air, take some exercise and enjoy fantastic views of the river, Fife and Dundee.
“But it is used by both cyclists and pedestrians and it is important that each group respect the other’s right to be there and to be aware of the potential seriousness of a collision.”
Councillor Taylor added: “In recent weeks there have been a number of near misses and this collision which no one wants to see a repeat of. The walkway is shared and with a little bit more awareness and caution everyone who wants to use it can do so safely.”