One month after the 11 September 2001 terror attacks, Nancy Pelosi, the House Minority Leader and California Democrat, wrote to Lieutenant-General Michael Hayden, then head of the NSA, to express her concerns.
The letter suggested that the security agency moved immediately after the attacks to identify terror suspects at home by loosening restrictions on domestic eavesdropping, The New York Times reported on Wednesday.
The letter was declassified at Pelosi's request.
Similar objections were expressed by John Rockefeller, Democratic senator from West Virginia, in a secret letter to Dick Cheney, the US vice president, nearly two years later.
In 2002, Bush signed an executive order authorising the security agency to eavesdrop without warrants on the international communications inside the US who the agency believed were connected to al-Qaida.
The disclosure of the spying programme last month provoked an outcry in Washington, and Congressional hearings are planned.
A Washington Post article on Wednesday, citing interviews with congressional and intelligence officials, reported that the secret domestic surveillance programme may have been operational even before the White House had received proper authorisation for it.
Cheney on Wednesday staunchly defended as "vital" the spying programme, saying that the domestic eavesdropping efforts have prevented acts of terrorism on US soil.
"The activities conducted under this authorisation have helped to detect and prevent possible terrorist attacks against the American people," he said.
"As such, this programme is critical to the national security of the United States," he said, according to a transcript released ahead of a planned speech in Washington.
"If we had been able to do this before 9/11, we might have been able to pick up on two of the hijackers who flew a jet into the Pentagon"
US Vice President
He said the existence of such a programme earlier could have prevented the September 11 terror attacks.
"There are no communications more important to the safety of the United States than those related to al-Qaida that have one end in the United States," the vice president said in his remarks to be delivered at the Heritage Foundation, a conservative think-tank.
"If we had been able to do this before 9/11, we might have been able to pick up on two of the hijackers who flew a jet into the Pentagon," said Cheney.
"They were in the United States, communicating with al-Qaida associates overseas. But we didn't know they were here plotting until it was too late."
The revelation last month about the wiretap programme run by the National Security Agency has sparked a political firestorm in the US, especially by civil libertarians who say that in authorising the program, President Bush has overstepped his constitutional limits.
Cheney said that the creation of the surveillance programme after the terror attacks on New York and Washington, which claimed some 3000 lives, was made "in a manner that is fully consistent with the constitutional responsibilities and legal authority of the president and with the civil liberties of the American people".