The sex attack happened in a ginnel in Yeadon at about 3pm on Wednesday (September 19).
The victim, 13, had been walking home from school when the man started following her in Gill Lane.
Police said she continued on to nearby Greenlea Road before running off into a ginnel between Greenlea Fold and Greenlea Close in the hope of losing him.
He approached the teenager in the ginnel and sexually assaulted her, before fleeing the scene.
Officers today issued an appeal to help in their efforts to find the man, and said patrols in the area have been stepped up.
Detective Inspector Amanda Wimbles, of Leeds District Safeguarding Unit, said: “This is obviously a very concerning incident and we are carrying out extensive enquiries to identify the person responsible.
“The suspect has followed the victim for a considerable distance and we would like to hear from anyone who saw a man fitting the description in the area around that time."
The attacker has been described as white, aged 30 to 40-years-old, and of skinny build.
He was wearing black clothing, including a black tracksuit top with the hood up. He had brown, unkempt hair and was clean shaven, with what appeared to be shaving cuts on his face.
The man spoke with a local accent.
Det Insp Wimbles added: “We are making checks on CCTV in the area and would ask anyone with CCTV camera who lives along the route the victim took to review their footage around the time of the incident.
“We recognise that an incident of this nature will cause understandable concern in the community and we are liasing with our colleagues on the local neighbourhood policing team who have been increasing their patrols of the area to reassure people.”
Anyone with any information is asked to contact police on 101, quoting crime reference 13180470386.
People can also call the independent charity Crimestoppers, anonymously, on 0800 555 111.