Bin Laden has been recording statements for the media
The decision came after a conference call between US national security adviser Condoleezza Rice and the heads of the networks.
White House spokesman Ari Fleischer said on Wednesday that broadcasts from suspected terrorists could contain anything from incitement to coded messages.
"I don't think the United States, which taught the world about freedom of expression, should now begin to limit it," chief editor Ibrahim Hilal told the Associated Press.
The US has recently put pressure on Qatar, where al-Jazeera is based, over the station's coverage.
Unedited broadcasts
Al-Jazeera has been the source of statements from Bin Laden and al-Qaeda spokesman Sulaiman Abu Ghaith which were shown in the US without being screened first by US broadcasters.
The messages lauded the 11 September attacks which killed more than 5,500 people and warned that more attacks would follow.
The networks have agreed not to show such statements again without reviewing them first.
The New York Times newspaper reported that the television executives said they had never before consulted one another as a group and made a collective policy decision about news coverage.
Mr Fleischer said broadcasting statements from the man the US holds responsible for the attacks on New York and Washington last month could not be in US interests.
"At best, this is a forum for ... propaganda inciting people to kill Americans. At worst, he could be issuing orders to his followers to initiate such attacks," he said.
Conference call
National security adviser Condoleezza Rice spoke to network executives by telephone conference call for about 20 minutes on Wednesday morning. They then stayed on to discuss the matter among themselves.
"Ms Rice made no specific request of news organisations, other than that we consider the possible existence of such messages in deciding whether and how to air portions of al-Qaeda statements," ABC said.
CBS echoed the tone of many of its colleagues in saying it was committed to "responsible journalism that informs the public without jeopardising American lives".
Matthew Felling of the Center for Media and Public Affairs, a media watchdog group, called the administration stance "a silky form of censorship".
He told the Associated Press that the White House position was "uncomfortable but understandable".
Coded messages
Network executives downplayed the likelihood of Bin Laden sending coded messages to "sleeper" agents in the US via news broadcasts.
"What sense would it make to keep the tapes off the air if the message could be found transcripted in newspapers or on the Web?" one anonymous executive asked rhetorically in The New York Times.
"The videos could also appear on the internet. They'd get the message anyway," the executive added.
There are historical examples of using news broadcasts to deliver coded messages.
During World War II, resistance fighters in Nazi-occupied France picked up secret messages in BBC broadcasts.