Nasa is to launch the space shuttle Discovery on 1 July, despite warnings from senior safety officials and engineers that it is not safe to fly.
Griffin (L) and Gerstenmaier are confident of the shuttle's safety
A meeting held to set the launch date was split on whether the problem of foam chunks breaking away - which brought down the Columbia - was fixed.
Safety officials said modifications carried out since the problem recurred a year ago were still not enough.
But managers decided to go ahead, insisting the crew was not at risk.
"There were very different viewpoints on the issue of whether we were ready to fly or not," US space agency (Nasa) administrator Michael Griffin told a news conference.
"I can't possibly accept every recommendation given to me by every member of my staff, especially when they all don't agree."
Reuters news agency, citing officials, said Nasa's top safety official and lead engineer both opposed the flight.
Some sections of the shuttle's protective foam have already been removed during the modifications, but the ongoing safety concerns focus on whether even more should be taken away, to ensure there is no repeat of the problem of sections breaking away.
Nasa managers reportedly urged that only one major modification should be made at a time.
The managers believe that even if more foam peels off, the crew will be able to take refuge on the International Space Station rather than attempting to land a damaged craft.
Nasa insists that the crew will not be put at risk
"We're not in the situation that we were in with during Columbia," Mr Griffin said.
On the Columbia, a large section of insulating foam broke away from the fuel tank during take-off in 2003, damaging the shuttle. All seven astronauts died when the craft burned up as it attempted to re-enter the Earth's atmosphere.
When Discovery blasted off last July in the first shuttle launch since the tragedy, more foam broke away - but this time did not do fatal damage.
Officials at the meeting chose the very first date from the launch window of 1-19 July.
"I don't see any reason why we could not launch 1 July," said Bill Gerstenmaier, the shuttle programme's associate administrator for space operations.
"We do not believe we are risking the crew."
On the mission, Discovery will fly to the International Space Station to deliver supplies and equipment. It will also drop off a new crew member, European Space Agency astronaut Thomas Reiter.
The crew arrived in Florida earlier this week to rehearse for the lift-off.