"Until these inquiries are complete, until the oversight's finished, I will be rendering no opinion from the podium," Bush said.
The White House has already denied it misled anyone on who knew about the CIA's action.
The New York Times newspaper recently reported that at least four White House lawyers had participated in talks with the CIA between 2003 and 2005 about whether the tapes should be destroyed.
The paper said the lawyers' participation indicated that White House officials were more extensively involved than the Bush administration has acknowledged.
Rights groups claim that the tapes have been destroyed because they provide evidence of torture techniques, such as simulated drowning known as waterboarding.
The White House says the tapes were destroyed to protect interrogators and that the US does not practise torture.
Citing an ongoing investigation by the justice department and the CIA, the White House refused to discuss the focus of the Times article: whether senior advisers to Bush were aware of the tapes.
Detainee is strapped to a board and water is poured over face covered with cloth or cellophane
Sensation is akin to drowning, with reflexive choking, gagging and feelings of suffocation
Variations include dunking detainee headfirst into waterin Central and South America 30 years ago
Dates back to the Spanish Inquisition and used
Condemned by rights groups as torture
Bush said the first time he learnt of the tapes was when Michael Hayden, the CIA director, briefed him this month.
On Wednesday, Dana Perino, the White House press secretary, reiterated Bush's assertion.
"He does not recall being told about the existence of the tapes, nor their destruction before being briefed by the CIA briefer," she said.
Michael Tarazi, a legal analyst, told Al Jazeera that if Bush were found to be involved in the destruction of the tapes, it would be an impeachable offence.
The Times reported that participants in the tape discussions included Alberto Gonzales and Harriet Miers, both former White House counsels; John Bellinger, then a lawyer at the National Security Council; and David Addington, a senior adviser to Dick Cheney, the vice-president.
The CIA admitted on December 6 that it had destroyed hundreds of hours of tapes, prompting an outcry from congressional Democrats and human rights activists.
A US federal judge is to hear testimony on Friday on whether the CIA violated a court order when it destroyed the tapes.
Henry Kennedy, a district court judge had ordered the hearing despite objections from the justice department which had said that in light of other government inquiries, a judicial inquiry was inappropriate.
The government has also sought delays in congressional attempts to investigate the tapes' destruction, saying they would hamper the justice department and CIA probe.
But on Thursday, the House of Representatives Intelligence Committee issued a subpoena for Jose Rodriguez, the former CIA official who directed that the tapes be destroyed.
The panel ordered Rodriguez, the former head of the CIA's National Clandestine Service, to appear for a hearing on January 16.
Legislators have accused the administration of trying to prevent the CIA from co-operating with their investigation.
Patrick Leahy, the Democratic chairman of the senate judiciary committee, accused the administration of "stonewalling".
"Every time we seem to reach a new low in this administration's arrogant flaunting of the rule of law and constitutional limits on executive power, we learn startling new revelations about the extent to which some will go to avoid accountability, undermine oversight and stonewall the truth," Leahy said.
The CIA gave congressional investigators access to its files on Thursday, inviting them to the agency's Virginia headquarters to begin reviewing documents and records related to the videotapes.