The victim was “left quite badly shaken” by the attack at her home in Hovingham Grove, Harehills, at 12.45pm yesterday.
According to West Yorkshire Police, she opened the door with the security chain on after hearing a knock, but couldn’t see anyone there.
As she began to open the door fully, a man barged in knocking her to the floor. He helped her to her feet and told her he was her cousin and that she knew him, detectives say.
The man began searching the house as the victim followed him around, begging him to leave. He then found her purse in the kitchen and removed an amount of cash before leaving through the front door.
He was described as white, aged in his late twenties, medium build, with short dark hair. He was wearing a grey, thick cable-knit jumper and black trousers.
Detective Sergeant James Entwistle, of Leeds District CID, said: “This was a really nasty offence against a vulnerable elderly lady who was left quite badly shaken by what happened.
“Although the victim received only minor injuries, the consequences could easily have been much worse given her age.
“We are keen to hear from anyone who has seen this man in the area or who has any information that could assist in identifying him.
“Officers are supporting the victim and looking at additional security measures to help protect her in future. The local neighbourhood policing team has been made aware of the incident and will be increasing patrols in the area.”
Anyone with any information should contact Leeds District CID via 101 or call the independent crime-fighting charity Crimestoppers anonymously on 0800 555 111.