Michael Hayden, director of the Central Intelligence Agency (CIA), said on Thusrday that the tapes were destroyed so that the identities of interrogators would not be compromised.
On Friday, leading Democrats called for inquiries into the matter by the justice department and congress and criticised the CIA for acting above the law.
Edward Kennedy, the Democratic senator for Massachusetts, spoke of a cover-up reminiscent of the Watergate scandal that drove Richard Nixon from the presidency in 1974.
In a speech on the senate floor, Kennedy said: "The past six years, the Bush administration has run roughshod over our ideals and the rule of law. Now, when the new Democratic Congress is demanding answers, the administration is feverishly covering up its tracks."
However, George Little, a CIA spokesman, said leaders of relevant congressional committees were told of the tapes, the CIA's plans to destroy them and that they had been destroyed.
The CIA's director said earlier that the agency's internal watchdog had watched the tapes in 2003 and verified that the interrogation practices recorded were legal.
But Marwan Bishara, Al Jazeera's senior political analyst, said the methods were actually torture.
Bishara said the fact that the CIA had the tapes but did not surrender them when a US commission to look into the 9/11 attacks and congress asked for such information, raised questions about whether the CIA obstructed justice.
Bush has been a strong defender of the CIA interrogation programme, saying it has produced intelligence that has helped capture al-Qaeda members and prevent attacks.
"The program is critical to the safety of the country," Dana Perino, the White House spokeswoman, said on Friday.
|"[Bush] has no recollection of being made aware of the tapes or their destruction before yesterday"|
Dana Perino, White House spokeswoman
Perino said Bush did not recall being told about the interrogation tapes or their destruction before he was briefed by Hayden on Thursday.
She said: "He has no recollection of being made aware of the tapes or their destruction before yesterday."
The destruction of the tapes comes amid scrutiny of the CIA's "rendition" programme, where suspects were allegedly detained and interrogated in secret locations outside the US.