The White House has bowed to pressure to allow National Security Adviser Condoleezza Rice to testify in public and under oath to the 9/11 commission.
The move is seen as a major change of position
President George W Bush said it would help give Americans "a complete picture" of events leading to the attacks on 11 September 2001.
The offer has been made on condition that it will not set a precedent.
Previously, officials had insisted that Ms Rice could only meet the commission in private for unsworn conversations.
They said a public appearance would contravene the constitutional separation of powers.
In a letter to the commission, White House counsel Alberto Gonzales said President Bush "recognises the truly unique and extraordinary circumstances" of the commission's job.
The White House recognises the "unique circumstances" of the commission's job
Mr Gonzales did not set a date for Rice's appearance but said "we can schedule a time as soon as possible".
The BBC's Justin Webb, in Washington, says the move is a U-turn of breathtaking proportions executed by a White House which is focused above all else on winning the president's re-election in November.
Last week, a former presidential security adviser, Richard Clarke, said the Bush administration had underestimated the terrorist threat because of a fixation on Iraq.
He said President Bush had pressed him to find a link with Saddam Hussein's regime in the hours and days following the 11 September 2001 suicide attacks on New York and Washington in which nearly 3,000 people died.
The issue has the potential to become a major embarrassment to the Bush administration.
Ms Rice is considered a key witness for the commission, which is looking into policy against the terror threat before 11 September 2001, and the response afterwards.
In a statement, the panel said the decision was a "significant contribution" by the president to the work of the commission.
Both the commission head and relatives of the victims of the attacks had demanded that Ms Rice testify.
According to polls, the American public did not approve of what some saw as constitutional nitpicking over Ms Rice's testimony.
It has been confirmed that President Bush and Vice-President Dick Cheney will also appear - in private - before the whole Commission.
They had been insisting on only meeting its leaders.
The White House is suggesting that it has won a concession, that none of this will set a precedent in any future investigation.
But our correspondent says that such a stipulation would be difficult to enforce and does not affect the current commission, which has, it seems, won this battle hands down.