A group of parents of many of those killed and injured in the rampage by student gunman Seung-Hui Cho issued a statement urging Kaine to reopen the review because of inaccuracies in the report.
The families' statement followed disclosure last week that the former director of the university's counseling center recently found missing mental health records for Cho at his home.
Cho committed suicide after killing students and faculty members in a dormitory and classroom building on the Blacksburg campus on April 16, 2007 -- the worst mass shootings in modern U.S. history.
"We still suffer emotional pain dealing with the impenetrable layers of bureaucracy in our simple quest for answers," the statement said. "An accurate, complete and thorough accounting of what happened before, during and after April 16th, 2007 is the legacy we seek on behalf of those who died and those who survived."
The families said they want more information about the discovery of Cho's records at the home of Dr. Robert C. Miller. Miller has said he inadvertently took the files as he left his job as director of Cook Counseling Center more than a year before the shootings.
Kaine said in response to a caller's question on his monthly radio show on Washington's WTOP that the professional staff who investigated and wrote the Virginia Tech Review Panel report is already investigating Miller's possession of Cho's records.
Reconvening the appointed members of the panel, including former State Police Superintendent Gerald Massengill and former Homeland Security Secretary Tom Ridge, would be a problem because all were volunteer members when they served.
"These records are critical. They never should have been removed from the counseling center. I want to know why," Kaine said.
Suzanne Grimes, whose son Kevin Sterne was wounded but survived, said she and other family members who have conducted their own investigation of the events of that day have found other errors in the report.
"With the revelation that Dr. Miller has discovered the missing records, it just raises whole new questions of what else is out there that we're unaware of," she said.
The review panel issued its report four months after the shootings, in August of 2007. A separate criminal investigation into the shootings is ongoing.
A telephone message left for Massengill was not immediately returned.
Associated Press writers Bob Lewis and Steve Szkotak contributed to this report from Richmond.