The team behind the private spacecraft, SpaceShipOne, says it will attempt the Ansari X-Prize in two flights on 29 September and 4 October.
The view from SpaceShipOne in space
The $10m (£5.7m) prize awards the first team to send a three-person craft over 100km, and repeat the feat in the same craft within two weeks.
SpaceShipOne, built by aviation pioneer Burt Rutan, became the first private manned craft to go to space in June.
Another 25 teams across the world are competing for the prize.
Although the fights have been scheduled, Rutan did not rule out the possibility of a third attempt if one of the other flights was not successful.
The two successful flights would have to take place before 13 October, according to the X-Prize rules.
A Canadian team of contenders, the da Vinci Project Team, also announced it was ready to show off its spacecraft, Wild Fire, on 5 August.
It said it intended to attempt the X-Prize later in the autumn, but no date was set.
"I'm pleased to announce that the first team is ready to make an attempt to claim the $10 million, with other teams close behind," said Dr. Peter H. Diamandis, Chairman and Founder of the X-Prize Foundation.
"The American Mojave Aerospace Ventures Team and the Canadian da Vinci Project Team are just two of the 26 competing groups who will someday make it possible for space flights to be conducted from commercial spaceports across the globe."
When the X-Prize is won, it is hoped it will usher in a new generation of commercial space travel.
Any team which attempts prize must give the X-Prize Foundation 60 days' notice.
Among the 25 others competing for the prize is the British civilian space project Starchaser Industries which plans to launch its own rocket in 18 months.
June's historic flight, a dry-run for the prize, saw SpaceShipOne carried to 46,000ft (13.8km) by its airborne launcher, White Knight, at which point it ignited its rockets to continue its journey alone.
It reached an altitude of 62.2 miles (100.12 km) earning astronaut wings for its civilian pilot, Michael Melvill.
There was some concern during the flight about a technical problem that had caused Melvill to use a back-up system to maintain control of the craft.
But the team, funded largely by Microsoft co-founder Paul Allen, discovered after extensive data analysis that it had been just "a brief lockout" which only lasted three seconds.
SpaceShipOne's X-Prize attempts will take place at Mojave Airport Civilian Aerospace Test Center in Mojave, California.