The statement was issued in response to recent news accounts on the health of Cronkite, 92, who became known as "the most trusted man in America" during his long tenure as anchor of "The CBS Evening News," E! Online reported Saturday.
"In order to dispel false rumors, Walter Cronkite's family want it known that, sadly, he is very ill and is not expected to recuperate; he is resting at home surrounded by family, friends and a wonderful medical team," the statement said. "We thank everyone for their prayers and good wishes."
Cronkite suffers from cerebrovascular disease, which affects vessels that supply blood to the brain.
A native of Missouri, Cronkite rose from World War II correspondent for United Press to become the CBS News anchor for 18 years.
During his tenure, he led the newscast to first place in the Nielsen ratings.
Cronkite's nightly signoff -- "And that's the way it is" -- became part of the popular lexicon.