Senior Democrats in the United States say the former vice-president Dick Cheney may have broken the law if he ordered the Central Intelligence Agency to conceal a counter-terrorism programme from Congress.
The chairwoman of the Senate Intelligence Committee, Dianne Feinstein, says Congress was told last month that Mr Cheney had issued that direct order. She says the failure to notify Congress is a big problem.
But a Republican senator, John McCain, says it is too early to discuss any formal investigation into the counter-terrorism programme, which never became fully operational.
The New York Times reported on Sunday that the CIA withheld information about the secret programme from Congress for eight years, on orders from Mr Cheney.
Citing two unidentified sources, the newspaper said CIA director Leon Panetta disclosed Mr Cheney's involvement in closed briefings to congressional intelligence committees late last month.
Senator Dianne Feinstein, chairman of the Senate Intelligence Committee, said Congress "should have been told" about the secret programme and that the vice president should not be above the law.
Intelligence and congressional officials told the New York Times the agency began the programme after the September 11 terrorist attacks and said it never became operational and did not involve CIA interrogation programmes or domestic intelligence activities.
Mr Cheney was a key advocate in the Bush administration of using controversial interrogation methods such as waterboarding on terrorism suspects. He has emerged as a leading Republican critic of President Barack Obama's national security policies.