The nearly airless planet is typically around 140 million miles from Earth and landing the first humans there, after a six- to nine-month journey, is an extremely ambitious goal for anyone.
Amazon.com founder Jeff Bezos's Blue Origin space venture is also designing a heavy-lift vehicle and capsule called New Armstrong, that will be capable of Mars transport, company President Rob Meyerson said.
The U.S. government is also stepping up efforts to venture beyond the moon.
In his remarks, Musk said there would be no guarantee of survival for anyone signing up with SpaceX for the "incredible adventure" of a trip to Mars.
"The risk of fatality will be high, there's no way around it. Basically, are you prepared to die, and if that's OK then you're a candidate for going," he said.
SpaceX intends to fly to Mars about every 26 months when Earth and Mars are favorably aligned for flight. Musk said he would like to land people on Mars as early as 2024. NASA's first human mission to Mars is expected about a decade later.
NASA is supporting SpaceX's first mission to Mars, which is targeted for launch in 2018. SpaceX wants to send an unmanned capsule, called Red Dragon, to the surface of Mars to test descent, entry and landing systems.
NASA will be providing deep-space and Mars communications relays for SpaceX and consulting services in exchange for flight data. NASA wants to be able to land payloads weighing up to about 30 tons on Mars. So far, the heaviest vehicle to land on Mars was the one-ton Curiosity Rover.