Rev. Jesse Jackson Not On Life Support Despite Reports

4:57 PM PT -- Rev. Jesse Jackson's family issued a statement late Sunday denying reports by CBS News and CNN that claimed he was on some form of life support in a Chicago hospital.

His family says in part ... "Reverend Jackson is in stable condition and is breathing without the assistance of machines. He remains under the care of physicians as he manages progressive supranuclear palsy (PSP), a neurological disorder with which he was diagnosed in April. Contrary to specific reports, he is not on life support.

Rev. Jesse Jackson is receiving a form of life support as his condition worsens in a Chicago hospital ... according to CBS News and CNN.

Sources tell CBS News the 84 year old civil rights leader has been on medication for several days to keep his blood pressure stable. The report says doctors are now attempting to wean him off the drugs, but his overall condition is said to be weakening.

Jackson is reportedly experiencing occasional moments of awareness though those windows have reportedly become less frequent. CBS News also reported family and friends are flying into Chicago to be at Jackson's side.

Jackson was admitted to the hospital last week after a recent diagnosis of progressive supranuclear palsy ... a rare neurodegenerative disorder similar to Parkinson’s disease.