Planning has been delayed by around three years, with the first manned SpaceX flight still pencilled in for July, though officials frequently refer to the end of 2019 as a more realistic deadline.
The Crew Dragon space capsule, launched from Cape Canaveral in Florida, is unmanned but it carries an astronaut test dummy named Ripley that is outfitted with numerous sensors to collect data from the flight.
The Boeing and SpaceX launch systems are aimed at ending United States reliance on Russian rockets for rides to the $100 billion orbital research laboratory, which flies about 250 miles (402 km) above Earth, at about $80 million per ticket.
The Falcon 9 blasts off, carrying Crew Dragon for the first time. No private company has ever launched humans into orbit, and during a webcast of the launch, SpaceX employees could be seen packed into the main foyer of the company's headquarters in Hawthorne, Calif., cheering each milestone.
In another success, the rocket's first stage returned to Earth, landing on a platform 500 kilometres off the Florida coast in the Atlantic.
Over the next 24 hours, the spacecraft will conduct a series of orbital phasing maneuvers. Early on Sunday morning, the capsule will dock with the ISS to drop off its cargo.
If it is able to dock successfully, the spacecraft would remain attached to the station for five days.
The key test flight is aiming to prove to NASA that astronauts will be safe on future flights.
"We're going to learn a ton from this mission, " said NASA's commercial crew program manager, Kathy Lueders. After NASA retired its shuttle fleet in 2011, the US has relied on Russian Federation to bring astronauts to and from the International Space Station.
Boeing aims to conduct the first test flight of its Starliner capsule in April, with astronauts on board possibly in August. But summer and fall came and went with neither spacecraft leaving the ground.
Boeing is also in the race to end NASA's eight-year drought of launching USA astronauts on US rockets from US soil.
Crew Dragon capsule, the company's very first vehicle created to carry people to space, is on the verge of flying humans to space, with a critical test flight underway.
Ripley - nicknamed in honor of the character played by Sigourney Weaver in the "Alien" movies - is fitted with monitors to test the forces that future astronauts will be subjected to on takeoff and when they return to the Earth's atmosphere and then land in the Atlantic, braked by giant parachutes.