South Yorkshire Police confirmed that the children – boys aged 13 and 14 – died following an incident at a house in Gregg House Lane, Shiregreen.
They were taken to hospital but were later pronounced dead. The cause of death has not yet been confirmed.
Four other children, aged 11, 10, three and a baby of seven months, were also taken to hospital, where they remain this afternoon while they receive treatment.
Commenting on the news on Facebook, people have spoken of their shock and sadness over the tragedy.
Joanne Higgins wrote: “Those poor innocent children, this is just heartbreaking RIP. What a cruel cruel world.”
Reacting to the news, Janice Smith said: “Utterly heartbreaking. Fly high with the angels boys. Taken way to soon my love sent to the other 4 children prayers are with you all xxx poor babies xx”
Others wished the four children in hospital well and spoke of the impact the news had on themselves and the wider community.
Adele Whyers wrote: “RIP to the 2 who have lost their lives. And I hope the other 4 children pull through in the hospital.
“Whatever has happened I hope the people responsible pay for what has gone off. Thinking of the family at this sad time.”
Lisa Baker added: “I don't know these children but this is truly heart breaking, in tears reading the news and the loss of two young lives.“I just can't comprehend or write how I feel.“I truly hope the 4 remaining children pull through this and get all the help, support and love they need to for now and their futures.“Their lives will truly be affected.“My thoughts are with all 6 children.”
And Jenny Bell commented: “Two children have died, let’s hope the others pull through and get the support they need.”
A 37-year-old man and a 34-year-old woman have been arrested on suspicion of murder in connection and remain in custody.