Rice told Fox News on Sunday the White House would cooperate should the justice department decide to proceed with a criminal investigation of the matter, which centred on the alleged public disclosure of the wife of former US Ambassador Joseph Wilson.
Wilson was sent by the CIA to Niger in 2002 to investigate a report that Iraq was trying to obtain uranium from Niger, but returned to say it was highly doubtful.
The Washington Post reported on Sunday that two top White House officials called at least six Washington journalists and revealed the identity and occupation of Wilson's wife - apparently in retaliation for his conclusion, which undermined the position of the White House.
The charge is now under review at the justice department, headed by US attorney general John Ashcroft.
On "Fox News Sunday," Rice, the top aide to US President George Bush said, "This has been referred to the justice department. I think that is the appropriate place for it."
The Post said CIA Director George Tenet sent a memo to the Justice Department raising questions about the alleged leak, which could mean prison time and a fine.
CIA Director George Tenet took blame for Bush's false claim that Iraq sought African uranium
Rice said, "I know nothing of any such White House effort to reveal any of this. And it certainly would not be the way the president would expect his White House to operate."
Bush made the Iraq uranium claim in his January State of the Union speech. Critics have said the Iraq-Niger assertion, which later was found to be based partly on forged documents, shows the administration has tried to hype intelligence to make a case for going to war.
Wilson said in August there had been several attempts to discredit him but mainly through an article by Chicago columnist Robert Novak that said two senior administration officials said Wilson's wife suggested sending him to Niger to investigate the uranium report.
Novak's column named Wilson's wife and said she was a CIA operative dealing with weapons of mass destruction.
Asked if the White House was not concerned that top officials might have done such a thing, Rice said she did not recall any discussions of the matter.
"I don't remember any such conversations," Rice said.
"It is well known that the president of the United States does not expect the White House to get involved in such things, anything of this kind," she added.
On NBC's Meet the Press, US congressman Richard Gephardt of Missouri, a Democratic presidential candidate, said Bush personally should "investigate what happened ... And people ought to be punished for doing this."
"We are trying to put now in place methods so you don't have to be dependent on people's memories for something like that"
US national security adviser
Rice also said top officials "didn't remember" in the case of the president's State of the Union address in January, in which he said, "The British government has learned that Saddam Hussein recently sought significant quantities of uranium from Africa."
Though the offending phrase had been deleted from an October presidential speech in Cincinnati, Rice said, "Three-plus months later, people didn't remember that George Tenet had asked that it be taken out ... I didn't remember. (Deputy national security adviser) Stephen Hadley didn't remember."
"We are trying to put now in place methods so you don't have to be dependent on people's memories for something like that," she added.