He said he has set up a "tiger team" to try to solve the problem as quickly as possible. "We don't expect this to be a long drawn-out affair," he said by telephone from Washington in a briefing with reporters in Houston.
Like other NASA officials, he said "we made a mistake" in not addressing the area of the external fuel tank where a piece of foam broke off shortly after Discovery's launch on Tuesday. That insulation chunk, which did not strike Discovery, came from a different spot on the huge fuel tank than the foam piece that ultimately brought down Columbia two years ago.
"Do I take responsibility? Absolutely," he said. "We'll fix this."
The launch windows later this year are very limited, however. The first is Sept. 9-24, and the second is a couple of days in November. That is based on the Earth's orbit and the hours of daylight a shuttle could be launched so it could be photographed to watch for problems.
Griffin said he was not willing to give up on this year.
In addition, he told reporters there wasn't just one, but perhaps four, pieces of foam that were bigger than NASA was willing to allow break from the fuel tank during launch.
A large piece of foam doomed Columbia on its launch in 2003 by hitting the shuttle's wing. The announcement by NASA on Wednesday that a similar piece of debris had unexpectedly snapped off Discovery led to the grounding of future flights until the problem is fixed. It was a disturbing setback for the agency, which had spent $1.4 billion and 2½ years of work to make the shuttles safer.
Earlier Friday, Discovery Commander Eileen Collins told The Associated Press she was "quite surprised" to learn about foam debris that could have damaged Discovery.
"Obviously, we're disappointed to hear about this," she said in the first of a series of interviews from space with radio networks.
"Personally, I did not expect any large pieces of foam to fall off the external tank," the commander told CBS Radio's Peter King. "I thought we had that licked." Hear full interview.
However, Collins said she's confident Discovery will get her crew home safely.
Astronaut Andy Thomas, who also was interviewed, said he didn't think the foam problem is "a fatal blow" to future shuttle flights. ... It's an emotional disappointment. It's also an engineering disappointment."
Added Collins: "I don't think we should fly again unless we do something to prevent this from happening again. The shuttle is due to be retired eventually, but we've got more years in them. ... I'm not ready to give up yet."
Discovery's astronauts spent Friday morning unloading 15 tons of supplies onto the space station. They also began yet another inspection of the shuttle for damage — this one about three hours. On Thursday, NASA reported that a smaller piece of foam may have hit a wing during liftoff.
CBS News Space Consultant Bill Harwood says Discovery's crew might have dodged a bullet when a piece of foam debris broke away from an aerodynamic ramp on the side of the ship's external fuel tank during launch Tuesday.