The court papers cited Lewis "Scooter" Libby, Vice President Dick Cheney's former top aide, as testifying Mr Cheney had told him that Mr Bush authorised him to disclose certain classified material to a reporter.
The disclosure revived a long-simmering political problem for President Bush who is struggling with weak poll numbers, an increasingly unpopular war in Iraq and a rebellion in his own Republican Party over issues such as immigration.
Democrats, who hope to seize control of Congress from Republicans in November elections, demanded an explanation but Mr Bush and the White House declined to discuss the disclosure.
"Our policy is not to discuss ongoing legal proceedings and that policy is unchanged," a spokesman, Ken Lisaius, said.
Mr Libby, who resigned from the administration last October, testified that he was specifically directed by the vice president to brief a reporter about the intelligence information and also about Joseph Wilson, a former ambassador who had criticised Mr Bush's Iraq policy.
Identity leaked
Mr Libby was charged with perjury and obstruction of justice by special prosecutor Patrick Fitzgerald, who is investigating the leaking of the name of Mr Wilson's wife, Valerie Plame, a CIA agent.
Mr Wilson has said White House officials deliberately leaked his wife's identity to pay him back for attacking the administration's Iraq policy.
The court documents made public on Thursday were filed by Mr Fitzgerald. They do not say that Mr Bush or Mr Cheney authorised Mr Libby to disclose Ms Plame's identity.
President Bush had the authority to declassify the material. But the court papers said Mr Libby noted "it was unique in his recollection" to get approval from the president, via the vice president, for such an action.
Mr Bush allegedly authorised the leak of classified material at a time when opponents were stepping up their criticism of the March 2003 invasion of Iraq after US forces had failed to find weapons of mass destruction there.
Mr Libby's indictment last October fuelled criticism that the Bush administration misled the American public over the reasons for the invasion.
The documents showed that Mr Libby told a federal grand jury he received approval from Mr Bush through Mr Cheney to discuss the classified Iraq material with then-New York Times reporter Judith Miller.
New York Democratic Senator Charles Schumer said he would formally request an explanation from the White House. "The more we hear, the more it is clear this goes way beyond Scooter Libby," he said.
"At the very least, President Bush and Vice President Cheney should fully inform the American people of any role in allowing classified information to be leaked."
Too many leaks
Mr Bush has often complained about leaks in Washington and vowed to take action against those who released unauthorised information to the public.
"There are too many leaks of classified information in Washington," he said after the Plame news broke in 2003.
"There's leaks at the executive branch, there's leaks in the legislative branch. There's just too many leaks. And if there is a leak out of my administration, I want to know who it is."
Mr Fitzgerald filed the 39-page document in opposing a request from Mr Libby to force the government to turn over additional documents.
He said some documents already provided to Mr Libby "could be characterised as reflecting a plan to discredit, punish or seek revenge against Mr Wilson".
Mr Libby's lawyers argued they needed certain documents to prepare to question some potential government witnesses.
But Mr Fitzgerald said prosecutors do not intend to call three of the individuals - former CIA Director George Tenet, White House national security adviser Stephen Hadley and Karl Rove, President Bush's main political adviser.
Mr Rove, the deputy White House chief-of-staff, remains under investigation in the Plame case. Mr Libby's trial has been set for January next year.