Two men, aged 79 and 59, were hurt along with a police officer during the incident in Moortown today.
It has now emerged that the 79-year-old man was bitten when he heard two dogs barking in his back garden on Garth Walk and went outside to investigate.
It is thought that the 59-year-old man, who also lives on Garth Walk, was then bitten in the street after the dogs ran out of the 79-year-old’s garden.
The animals are believed to have originally got loose from a property near Garth Walk.
Police were called to the scene at about 4.40am, with an officer suffering a serious bite injury to his arm while trying to bring one of the dogs under control.
The 59-year-old resident’s injuries are said to be “potentially life-changing”.
All three men are continuing to receive treatment in hospital.
Two people have been arrested and both of the dogs seized by police.
Leeds CID’s Det Insp Richard Holmes said: “We appreciate there will be understandable concern in the community following this incident.
“We will have extra police patrols in the area to offer reassurance, and I would urge anyone who has any concerns to speak with officers.
“Our enquiries remain ongoing into the circumstances and I would ask anyone who has any information to contact police.”