SpaceX will decide later whether to try to catch the top part of its huge Starship rocket as it returns to Earth.
The company had hoped to catch both the bottom and upper stages of the rocket using mechanical arms - nicknamed chopsticks - on its launch tower.
But the first catch of the rocket's booster was aborted a few minutes after the launch, and instead the booster diverted to the ocean, bursting into flames just above the sea.
The top part, known as the Ship, is due to return to Earth at about 15:15 local time (21:15 GMT) on Saturday.
This is the 15th test of Starship and the first that hoped to fully recover both parts of the rocket. SpaceX wants to make the top and bottom sections of Starship fully reusable so it can fly repeatedly and reduce costs.
The 124m-tall (407ft) rocket successfully blasted off from the Starbase launchpad in Boca Chica, Texas at 16:47 local time on Friday.
The plan was to grab the bottom part of the rocket - the Super Heavy booster - six and a half minutes later when it returned.
A "go" was initially given by mission control for a catch attempt at the launch tower, but the booster activated an automated abort, diverting instead to the ocean where it hovered above the water before exploding.
During a livestream of the launch, a SpaceX spokesperson said: "Safety is always the number one priority and we're still testing out things that we haven't done before on these vehicles, and so we are prioritising making sure that we can perform each manoeuvre safely."
The top part of the rocket continued its journey to space where it deployed 26 satellites, which form part of the Starlink constellation that provides high-speed internet.
The Ship is due to complete 14 orbits around the Earth before returning to the launch tower 22.5 hours after taking off.
SpaceX has managed to catch the Super Heavy Booster on three earlier test flights.
But the upper stage of the rocket, which only reached orbit for the first time in September, has never been grabbed by the "chopsticks".
Before the flight, SpaceX said it would only decide to try to catch the Ship after carefully assessing the vehicle while it was in space.
If any problems are detected, there are various points during the flight when the rocket stage can be brought down in the ocean.
Building a fully reusable rocket is a long-held ambition for SpaceX.
In 2015, it became the first company to vertically land part of a rocket with its Falcon 9 booster.
Falcon 9 rockets now fly more than 100 times a year and the ability to reuse the bottom part of the rocket has dramatically cut the costs of launch.
But landing an entire Starship rocket could take this to the next level, says Prof Malcolm Macdonald, president of Royal Aeronautical Society.
"Full reusability has the potential to fundamentally change the economics of accessing space," he said.
"One successful flight will not prove that model, but it could mark an important transition: from demonstrating that Starship can fly, to demonstrating how Starship could operate."
After SpaceX became a public company earlier this year, its shareholders will be carefully monitoring this flight, as will Nasa.
The progress of Starship has direct implications for Nasa's attempt to land humans on the Moon in 2028 - a highly ambitious timeline.
SpaceX has been given a Nasa contract to configure the Ship into a lander that will eventually take astronauts down to the lunar surface.
But it is not the only company working with Nasa. Blue Origin, owned by rival tech billionaire Jeff Bezos, also has a contract to use its New Glenn rocket and lander for the Moon touchdown.
Both companies will also play a key role in the Artemis III mission, which is currently planned for summer 2027 - another challenging schedule.
Four astronauts in Nasa's Orion spacecraft will attempt to dock with both SpaceX and Blue Origin's landers during the voyage.
Starship will need to make a lot of progress in the coming months to meet these commitments - the pace of the rocket's development has been far slower than SpaceX had intended.
But Blue Origin also has much work to do. The company suffered a major setback earlier this year when its rocket exploded, totally destroying its launchpad in Florida.
Blue Origin had said its spacecraft would be back in action by the end of this year, but a return to flight has now been delayed to early in 2027.
Nasa is under pressure to meet its timelines. Its administrator Jared Isaacman has said the US was in a race with China to get to the Moon. China plans to land its Taikonauts on the lunar surface by 2030.
