Cuccinelli, a climate change skeptic, is seeking the documents for an investigation into whether Mann defrauded taxpayers by using manipulated data to obtain government grants.
Global-warming deniers have targeted Mann for his research that shows that the earth's temperatures have risen steadily since the early 1900s. Two U.S. university reviews have cleared Mann of wrongdoing.
A judge ruled in August that the attorney general was not specific enough about how Mann might have broken the law, and that he lacks authority to investigate federal grants.
Cuccinelli's office submitted what it called a scaled-down request and more specific language.
A spokesman for Cuccinelli said Thursday the revised filing is "consistent with the judge's ruling in August."
"The e-mails and documents requested are all property belonging to the Commonwealth of Virginia," said the spokesman, Brian Gottstein. He said the attorney general is not seeking any of Mann's private documents.
In their filing Wednesday, however, attorneys for the university said Cuccinelli's revised request mirrors the previous, thwarted attempt.
The filing, the attorneys wrote, "constitutes an unprecedented and improper governmental intrusion into ongoing scientific research."
The university's request was filed Wednesday in Albemarle Circuit Court.
A university spokeswoman said the university's request for a delay is intended to give the Supreme Court a chance to rule before litigating the case anew.
In an e-mail to The Associated Press, Mann, who now works at Penn State, wrote, "I am pleased that University of Virginia has chosen to continue to stand up to Mr. Cuccinelli and his misguided witch hunt."
The university said it has run up a $350,000 tab for legal fees, which has been paid in private funds.
The university has argued that Cuccinelli's actions could have a chilling effect on academic freedom and scientific research.
University officials and others have said the investigation is an attempt to take aim at Mann's conclusions rather than to uncover fraud.
Cuccinelli has denied that he is targeting Mann's conclusions, and likened his effort to pursuing a private vendor for submitting false receipts to a state agency for reimbursement.