The director of the CIA has been questioned by Congress over the wiping of videotaped interrogations amid fears over a possible a torture cover-up.
Gen Hayden has spoken out to say the CIA did nothing wrong
Gen Michael Hayden told the House intelligence committee the CIA "could have done an awful lot better" in keeping Congress informed on the issue.
He said he had no prior knowledge of plans to destroy the tapes.
Lawmakers said former CIA directors would also be summoned to testify in the investigation.
Gen Hayden confirmed last week that the CIA had destroyed footage of two interrogations, saying the tapes were no longer of intelligence value and to protect the identities of agents.
Correspondents say there are suspicions that the decision was made to conceal evidence that terror suspects were being tortured.
The CIA and the US justice department are also investigating the tape destruction.
The interrogation tapes were made in 2002 and destroyed in 2005, a year before Gen Hayden was appointed director of the CIA.
But the director has come under pressure to explain the agency's decision to destroy the tapes.
He has defended the decision, saying it was "done in line with the law".
Gen Hayden was questioned by the House of Representatives select committee on intelligence on Wednesday, a day after testifying before its Senate counterpart.
He said he was unable to answer some of the lawmakers' questions, and would arrange for people who were more involved at the time to appear before the committees.
The House committee's chairman, Silvestre Reyes, a Democrat, said Gen Hayden had promised "a full and complete accounting and record of everything that's available".
He said Gen Hayden's predecessors George Tenet and Porter Goss would be called to testify, as well as John Negroponte, formerly Director of National Intelligence, now Deputy Secretary of State.
Wednesday's meeting came a day after a former CIA-agent said that water-boarding - a technique that simulates drowning - had been successfully used on one al-Qaeda suspect.
John Kiriakou told US broadcaster ABC that suspected al-Qaeda chief recruiter Abu Zubaydah, had cooperated after he was subjected to the practice.
Abu Zubaydah is understood to be one of the men who was shown in the deleted footage.
Human rights groups say that water-boarding - and other techniques allegedly used by the CIA - can be defined as torture under various international treaties to which the US is a signatory.
The Bush administration has always maintained that it does not allow the use of torture.