"Face the Nation" host Bob Schieffer (search) will be sitting in the anchor chair after Rather's last night on Wednesday until the network decides on a permanent replacement.
"Although Dan did a fine job, I would have liked to have seen (Schieffer) there a long time ago," Cronkite said Monday during a cable news interview. "He would have given the others a real run for their money."
Cronkite called Schieffer "one of the great television journalists of our time."
Rather, 73, ends his run as evening news anchor Wednesday, exactly 24 years after replacing Cronkite. Cronkite said it was a tribute to Rather that he held on so long.
"It surprised quite a few people at CBS and elsewhere that, without being able to pull up the ratings beyond third in a three-man field, that they tolerated his being there for so long," Cronkite said in the interview.
But Cronkite did not heavily fault Rather for his role in last September's discredited story about President Bush's military service. Rather anchored the "60 Minutes Wednesday" story.
"We all know he made a mistake by now," Cronkite said. "But would we have done much the same? I would not be sure that I wouldn't have followed my producers and accepted what they had to offer."