Rockefeller is chairman of the Senate Intelligence Committee. In an interview with McClatchy Newspapers, he said Cheney leaned on the former chairman, Sen. Pat Roberts, R-Kan., in an effort to delay the committee from reaching any conclusion.
There was "constant" pressure on Roberts, Rockefeller said.
Cheney's office, in an e-mail, said there was no truth to the charge.
"The vice president believes Sen. Roberts was a good chairman of the Intelligence Committee," a spokeswoman said.
The committee released its Phase I report in 2004, which concluded that the CIA and other agencies supplied erroneous information. Its Phase II reports are still incomplete.
Rockefeller also said he believes the Bush administration's warrantless wiretapping program is illegal.
Notable deaths of 2014 [PHOTOS]