Would-be space tourists have applied to Virgin Galactic for refunds following last month's doomed test flight.
Company chief executive George Whitesides said "a few" of its 800 customers have pulled out of taking part in a future mission into space.
It comes after co-pilot Michael Alsbury died when the test flight aircraft crashed in the Mojave Desert in California on October 31.
Surviving pilot Peter Siebold was said to be alert and speaking with family members and medical staff in hospital days after the fatal launch.
Virgin Galactic, owned by Sir Richard Branson's Virgin Group and Aabar Investments PJS of Abu Dhabi, plans to fly passengers to altitudes more than 100km above Earth.
In an interview with the Daily Telegraph, Whitesides said he wasn't surprised by the refund requests.
"I think what is relevant is that the vast majority have said 'Don't give up, keep going, we're with you'," he said.
"So 97 per cent have been very supportive, but a few people have asked for a refund.
"My resolve is unshaken. I have always known that this would be a challenge."
The company, which sells seats on each prospective journey for $US250,000 ($A270,500), has denied reports that it ignored safety warnings ahead of the test flight crash.