Discovery and its seven-member crew were scheduled to lift off from Kennedy Space Center at 3:49 p.m. ET. Sunday's liftoff is scheduled for 3:26 p.m. ET. They can keep trying until July 19.
Thunderstorms and heavy clouds had weather forecasters concerned enough they gave Discovery a "no go" for launch at 3:41 p.m.
"Steve, sorry to break your string. We're not going to make it today," mission control told STS-121 Commander Steve Lindsey.
All week the weather had been unpredictable. This launch would be only the second shuttle flight since Columbia disintegrated over Texas in 2003.
Discovery is to embark on a 12-day mission to the international space station.
The shuttle will deliver supplies to the space station and drop off European Space Agency astronaut Thomas Reiter, who will join the Expedition 13 crew members already there.
Two astronauts, Piers Sellers and Mike Fossum, will conduct two space walks to test a new shuttle robotic arm and to repair a damaged piece of equipment outside the space station.
They may also do a third space walk to test repair techniques on the shuttle's thermal protection system.
Earlier Saturday mission managers decided a problem with a thermostat in one of Discovery's thrusters, which was showing a reading in the 80s when it should have been in the 60s, was not dangerous and it could be fixed once the shuttle was in orbit.
The thermostat was monitoring one of the shuttle's 38 primary thrusters used to maneuver the orbiter in space, including docking it to the international space station.
NASA's decision to resume shuttle flights this summer is not without controversy.
In the weeks leading up to the launch two NASA officials, chief engineer Chris Scolese and chief safety officer Bryan O'Connor, gave a "no go" for launch.
Charlie Camarda, an astronaut who flew on the shuttle mission last summer and who is the top engineer in Houston, Texas, was reassigned this week after allegedly rubbing senior managers the wrong way and expressing reservations about mission safety.
But Griffin said Friday Camarda's reassignment had nothing to do with the mission -- simply that he was needed elsewhere.
A 1.6-pound piece of insulating foam broke loose from Columbia's external tank during its launch fatally damaged the wing, an accident investigation board concluded.
The spacecraft broke up when superheated gases entered the damaged wing upon re-entry into the atmosphere. All seven astronauts aboard died.
NASA spent nearly two and a half years redesigning the tank and overhauling its culture.
Program manager Wayne Hale said NASA engineers have learned a lot about foam dynamics in the past year but there is still no way to completely stop the foam from flying off the tank.
"Foam will come off. There's no way around that. It is an expected event," said John Chapman, NASA's external tank project manager. "Our objective is to make sure if it does come off, it comes off in small enough pieces that it doesn't cause any harm."
O'Connor and Scolese are specifically concerned about three dozen pieces of foam on Discovery's external fuel tank -- so called ice-frost ramps.
Small pieces of foam have come off the ice-frost ramps on previous flights. And in a worst-case scenario, small pieces of foam debris from the ice-frost ramps could cause critical damage to the orbiter, according to wind tunnel test results conducted by NASA this spring. Even so, NASA officials have put off structure modifications until after the launch.
Griffin called the disagreements with the technical fixes a good sign that the culture at NASA has changed. The agency was faulted by the Columbia investigation board with having a conformity of opinion.
"I personally want every engineer to express the best opinion that they can give us," Griffin said.
He and top senior officials took into consideration O'Connor and Scolese's concerns but concluded that if falling foam damages Discovery, engineers will know about it this time and the crew can take refuge on the space station -- pending a rescue mission.
Griffin said he wants to fly now because the shuttle program is slated to end in 2010 and NASA is committed to flying at least 16 missions to complete the space station.
He worries delays now will lead to dangerous schedule pressure later on.
"Flying the shuttle is not without risk for many reasons beyond foam. In fact, I worry we spend so much time worrying about foam that we won't worry about other things that could get us," Griffin said. "But we've tried to address them all."
"I very strongly feel that we are not risking crew for foam in this case or I won't feel comfortable launching."
Lindsey said he and his crew understand the risks and are ready to fly.
"We've been training for an awfully long time," Lindsey said. "We're as prepared as we're ever going to be."