"At best, Osama bin Laden's messages are propaganda calling on people to kill Americans.
"At worst, he could be issuing orders to his followers to initiate such attacks."
Fleischer admitted there was no evidence to support this theory.
But the networks each said yesterday they would ban live cover of al Qaeda messages and promised self-censorship, ranging from not screening the tapes to reviewing them in full before broadcasting them.
The White House and the television news executives said Rice had not ordered them to ban the broadcasts, but to "exercise judgment" in using them.
But the phone call has been widely interpreted by other news organisations as the first clearcut example of censorship in the war against terror - and an illustration of what happens when freedom of speech and fears over national security collide.
Rice was referring to two al Qaeda broadcasts which have been replayed around the world since the United States launched its attack on Afghanistan.
In the first, apparently made before the US raids began, bin Laden appeared in daylight against a rocky backdrop, wearing a white Afghan headdress with an American-style camouflage jacket and clearly showing off a large wristwatch as he spoke into a handheld microphone.
After thanking God for the September 11 attacks on the United States, he said: "I swear to God that America will not live in peace before peace reigns in Palestine, and before all the army of infidels depart the land of Mohammad, peace be upon him."
The second broadcast, aired in unedited form on Tuesday by CNN and NBC's cable network, showed al Qaeda spokesman Abu Ghaith praising the September 11 attacks and warning that more could come.
Fleischer said yesterday that the pre-recorded tapes could serve only the interests of al Qaeda.
Since bin Laden was the target of a high-tech global manhunt, he could not simply pick up the phone to activate his network. It was logical to expect he might hide instructions in taped public messages.
There was little supporting evidence afterwards from the Washington press corp's usual off-the-record sources.
Administration officials said CIA analysts studying the broadcasts detected nothing specific, but made a compelling enough argument about the messages risk for the Administration to get Rice on the phone to TV executives as soon as possible.
One said the suspicion was based on hunch and common sense, because bin Laden's language was filled with flowery, fuzzy images.
Another noted that bin Laden and his spokesman wore white turbans, the Muslims' traditional colour of martyrdom.
Terrorism and security experts said a signal for action could have been anything from bin Laden's clothes to a hand gesture or a particular verse of the Koran.
But they were sceptical about whether the al Qaeda leader needed to use any code words, as his Sunday speech was already an open declaration of holy war.
They also questioned whether he would rely on a relatively uncontrollable form of communication to pass operational messages to sleeper cells.
But the theory has historical precedents. During the Second World War, resistance forces inside Nazi-occupied France knew to listen for coded phrases in the speeches of British Prime Minister Winston Churchill broadcast over the BBC.
For American television networks, Rice's extraordinary call highlighted the age-old issue of media censorship - and self-censorship - in wartime.
Yesterday, CNN said it had decided not to replay the words of the statements.
But it would show excerpts of the tape without sound for illustrative purposes.
The conservative Fox News Channel went further, banning all video grabs from the tapes and declaring: "These are plainly propaganda messages being distributed for as much circulation as possible by a terrorist organisation. We will no longer act as a transmission belt for propaganda of the al Qaeda organisation."
The BBC said it would not show any al Qaeda or bin Laden statements in full.
In New Zealand, TVNZ and TV3 said they had received no warnings and saw no reason to restrict their cover of bin Laden's messages.
The usual rules of press freedom have already come under fire in the United States since the September 11 attacks.
Last month, Fleischer publicly scolded the host of TV's Politically Incorrect talk show for controversial comments on the terrorist attacks and admonished all Americans "to watch what they say" - an echo of the Second World War "careless talk costs lives" slogan.
Yesterday, US media commentators took a sympathetic line to Rice's request.
At the Center for Media and Public Affairs, a media watchdog group, director Matthew Felling called the Administration's request "a silky form of censorship ... uncomfortable but understandable".
"Because bin Laden is resourceful, he would use our cultural tools as weapons, be they airplanes or airwaves."
And a media columnist at the normally liberal Washington Post, Howard Kurtz, questioned whether terrorists such as bin Laden deserved the right to be heard.
"We should continue to strive for balance in our international coverage," he said.
"We should continue to try to understand those who despise the West. But deadly terrorism cannot be transformed into just another view, or its proponents just more guests on the talk show circuit."
In New Zealand, Canterbury journalism school head Jim Tully strongly disagreed, saying it was ironic that the United States, which regarded freedom of speech as so essential to democracy, was resorting to censorship of bin Laden.
He said the only justification would be if American officials told the media they had firm evidence that bin Laden was using the tapes to activate his agents.
Responsible news organisations would then hold back in good faith, as they had often done before.
But without such proof, the words "national security" should be viewed with suspicion, as censorship was "a slippery slope".
Similar scepticism about American motives came from the news head of the Arab television station which brought the bin Laden tapes to the world.
Ibrahim Hilal, chief editor of Al Jazeera in Qatar, scoffed at the notion of hidden signals and said the terrorists were sophisticated enough to communicate with each other directly.
"I don't think the United States, which taught the world about freedom of expression, should now begin to limit it."
Al Jazeera, which has 350 staff in more than 35 offices from Washington to northern Afghanistan, has been enjoying international fame as the only media outlet with a correspondent and cameras in Kabul.
It is giving the world the only pictures of the American bombing raids.
But Al Jazeera is now facing its own censorship pressure from the United States.
Secretary of State Colin Powell complained to the Emir of Qatar last week about the station, which he describes as a virtual mouthpiece of al Qaeda.
State Department officials have complained that it carries "inflammatory" and "totally untrue" stories.
The tough talking has been undercut by an admission that President Bush may follow the example of British Prime Minister Tony Blair and give an interview to the top-rating station.
It has 40 million viewers and a reputation - in the words of the Independent's veteran Middle East correspondent Robert Fisk - for producing "the most original, toughest reporting ever in the Arab world".
Luckily for Al Jazeera, Qatar's Emir Hanad remains defiantly against American pressure to censor the station.
The Emir pointed out in Washington yesterday that Qatar was embarking on a parliamentary life with a democracy "which dictates that freedom of the press should be granted and that press should enjoy credibility".
Map: Opposing forces in the war against terror
Afghanistan facts and links
Full coverage: Terror in America
