New information has come to light relating to investigations across 13 institutions as well as "reference to other hospitals", the Health Secretary said.
He has asked police to review all of the evidence before relevant information is passed to investigators "as quickly as possible".
Investigations began earlier into activities at Broadmoor, Stoke Mandeville and Leeds General Infirmary, along with inquiries at 10 other trusts following the abuse revelations last year.
Mr Hunt said any hospitals involved would be named after a review of the new potential evidence.
"We understand the material includes information about hospitals where investigations are already under way and reference to other hospitals," he told Parlia-ment. The final reports of the investigations are now expected by June next year.
Mr Hunt said: "This additional material means the timetable will be affected."
Savile, who died in 2011 aged 84, is believed to have abused hundreds of children. He had a bedroom at Stoke Mandeville Hospital, an office and living quarters at Broadmoor, and access to Leeds General Infirmary.
Liz Dux, head of abuse at Slater and Gordon Lawyers, which represents 72 potential victims, said: "The news that the time-frame for concluding the investigation has been extended will be met with dismay. My clients all need closure."