In a letter made public Friday, Intelligence Chairman Peter Hoekstra, R-Mich., and the panel's top Democrat, California Rep. Jane Harman, asked Goss to reveal as much of the report from his inspector general as possible.
"We believe the public has a right to know if people should be held accountable for those failures as a result of gross negligence or misconduct," Hoekstra and Harman wrote on Sept. 6. "More importantly, the public also should know what steps should be taken in the future for the CIA to address the findings of the report."
Spanning hundreds of pages, the report calls for disciplinary reviews for former CIA Director George Tenet and current and former officials who were involved in faulty intelligence efforts before the attacks.
The report was sent to Congress last month. Limited details have been provided by anonymous officials.
"The office of the inspector general developed this report over two years. During that same time period, much has been done at CIA and throughout the intelligence community to improve and reform the way we do business," agency spokeswoman Jennifer Millerwise Dyck said.
She would not comment further on whether the report would be declassified.
Senate Intelligence Chairman Pat Roberts, R-Kan., has also sent a letter to Goss requesting the report's declassification. An aide declined to provide a copy of the correspondence.
A spokeswoman for the Senate committee's top Democrat, West Virginia Sen. Jay Rockefeller, said he supports Roberts' request.
Such bids for disclosure could put Goss in a tight spot. As a chairman of the House Intelligence Committee, he helped lead a congressional inquiry into the attacks and requested the inspector general's investigation.
However, a public report could attract more negative attention to the agency, which has come under fire for 9/11 and the prewar intelligence on Iraq.