By Andy Pasztor

Elon Musk's SpaceX safely launched two NASA astronauts from a Florida pad, kicking off a new era of corporate-driven space missions and propelling the capsule on what is scheduled to be a 12-minute ride to initial orbit.

No company has ever flown commercially developed hardware carrying humans and linked up with the international space station, which is the aim of Saturday's long-anticipated mission. If Space Exploration Technologies Corp. reaches that goal Sunday as planned, it will demonstrate a major shift in the country's space endeavors and mark the first human launch from U.S. soil since 2011. It also would be a long-awaited milestone for NASA and a resounding achievement for SpaceX and its billionaire founder, Elon Musk.

Considered the riskiest portion of the ascent, a Space Exploration Technologies Corp. Falcon 9 rocket lifted off from Kennedy Space Center precisely as planned at 3:22 p.m. ET. The 230-foot booster roared to life after a smooth countdown, carrying a gumdrop-shaped capsule and representing America's evolving space ambitions.

Before heading to the pad, the astronauts had a final chance to wave at family members as the two of them left a crew facility. They rode to the pad in a white, electric-powered sedan festooned with NASA logos and built by Tesla Inc., another of Mr. Musk's companies.

Roughly three hours before liftoff, Messrs. Behnken and Hurley entered the capsule, settled into their places, donned their seat restraints and eventually the hatch was sealed behind them.

Less than an hour before scheduled liftoff, SpaceX flight controllers declared the mission was "go for launch," and fuel started loaded about 35 minutes before launch. Roughly 10 minutes before launch, a SpaceX controller wished the crew good luck and added, "enjoy those views of our beautiful planet."

The technically smooth countdown had its share of suspense nonetheless, as weather forecasts hours before predicted only a 50-50 chance of acceptable weather conditions. Rain and high-level winds pose hazards for rockets, and SpaceX staff also monitored weather conditions at dozens of sites around the world in case the astronauts had to separate from the rocket en route for an emergency descent.

President Trump and Vice President Mike Pence watched the liftoff from the Kennedy Space Center. "I think I have an obligation to be there," Mr. Trump said, upon leaving the White House shortly after noon to head to Florida.

The National Aeronautics and Space Administration has spent years trying to shift away from the lumbering process of building and designing government-owned spacecraft and toward using public-private partnerships to develop vehicles and then pay private contractors for specific services.

A successful launch Saturday would mean NASA astronauts won't have to piggyback on Russian rockets and spacecraft, as they have since the aging U.S. space-shuttle fleet was retired nine years ago. Looking ahead, NASA and White House officials envision emphasizing deep-space exploration as part of a commitment to relying on similar corporate-government teams. Those would include company-led endeavors, with relatively limited federal oversight, taking astronauts to the moon as soon as 2024 and later to Mars or beyond.

Some longtime NASA watchers see the current mission as a crucial steppingstone, perhaps as significant in some ways as the Gemini missions of the mid-1960s that paved the way for the Apollo moon landings. But this time, making the government "a customer rather than operator is as astonishing as it is bold for NASA," said Mark Albrecht, a former White House space adviser and retired senior industry executive. "NASA will take the blame for failure and allow SpaceX to receive most of the glory of success."

Beyond the policy changes and revamped contracting arrangements, the sheer promise of accelerating human space exploration excites many government and industry officials. Nothing generates as much pride as adding humans to the equation.

"When you put an astronaut on top of a rocket, that changes everything," Air Force Gen. John Hyten, a longtime space expert and vice chairman of the Joint Chiefs of Staff, told a White House space-policy council.

The Crew Dragon capsule, featuring automation supplemented by touch-screen controls similar to those found on the dashboards of electric cars, has suffered a series of setbacks, including balky oxygen generators, malfunctioning thrusters and problematic parachutes. After its planned launch Saturday, the capsule is slated to stay at the international space station for around two months. If all goes well, including the return trip that ends with a splashdown in the Atlantic, NASA hopes for swift approval of SpaceX's systems as space taxis that would ferry crews to and from orbit.

"Human space flight is really, really tough," said Benji Reed, director of crew mission management at SpaceX. As company and NASA engineers work together to identify and alleviate risks, he said, "we are all holding each other accountable."

Boeing Co. has developed a rival capsule, the Starliner, which has struggled with its own technical challenges and might make a test flight later in the year without astronauts.

NASA has invested more than $7 billion of taxpayer money so far in SpaceX and Boeing efforts to resume astronaut liftoffs from U.S. soil. The agency's Mr. Bridenstine sees a successful launch as recasting the path for America, other nations and industry to reach space.

U.S. astronauts "need to have the capability of accessing space, not just for NASA but for all of humanity," he has said.

Write to Andy Pasztor at andy.pasztor@wsj.com