The children and a woman were bitten by a dog in the Rumer Hill area of the town on Saturday lunchtime.
An eight-year-old boy suffered a "serious facial injury" and a six-year-old girl suffered an arm injury, Staffordshire Police said.
Both children were taken to Birmingham Children’s Hospital for treatment. The woman was bitten on her arm but did not need hospital treatment.
The attack happened on The Ridings, a residential road off Brook Vale, where emergency services were sent at 12.40pm.
Police officers remained at the scene throughout Saturday afternoon, with a forensic investigation van parked outside a house where around five officers were stationed.
Nobody is believed to have been arrested and it has not yet been confirmed if the dog has been seized.
Staffordshire Police is appealing for witnesses to come forward and urged anyone with information to contact the force on 101 quoting incident number 360 of March 26.