The six-legged Athena, carrying 11 payloads and scientific instruments, targeted its landing site some 160 km from the lunar south pole for touchdown on Thursday.
But by that time, the lander's engine was still running, telemetry showed, as it appeared to hover over the moon. Minutes later, after commanding the lander's engine to shut down, the company confirmed Athena "is on the surface of the moon," but its exact orientation was unclear.
Intuitive Machines ended its mission live stream and said a press conference is scheduled for later in the day.
Intuitive Machines' shares fell more than 20 per cent in afternoon trading. The stock has more than doubled in the past year.
The space startup is one of many companies primed by NASA to return the United States to the moon. The focus on private companies is seen as lower cost but higher risk.
After launching atop a SpaceX rocket on February 26 from Florida, Athena has flown a winding path to the moon some 383,000 km away from Earth.
The Houston-based company's first moon landing attempt almost exactly a year ago, using its Odysseus lander, marked the most successful touchdown attempt at the time by a private company.
But its hard touchdown - due to a faulty laser altimeter used to judge its distance from the ground - broke a lander leg and caused the craft to topple over, dooming many of its onboard experiments.
Five nations have made successful soft landings in the past - the then-Soviet Union, the US, China, India and, last year, Japan. The US and China are both rushing to put their astronauts on the moon later this decade, each courting allies and giving their private sectors a key role in spacecraft development.
India's first uncrewed moon landing, Chandrayaan-3 in 2023, touched down near the lunar south pole. The region is eyed by major space powers for its potential for resource extraction once humans return to the surface - subsurface water ice could theoretically be converted into rocket fuel.
Austin-based Firefly Aerospace this month celebrated a clean touchdown of its Blue Ghost lander, marking the most successful soft landing by a private company to date.
Intuitive Machines, Firefly, Astrobotic Technology and a handful of other companies are building lunar spacecraft under NASA's Commercial Lunar Payload Services program, an effort to seed development of low-budget spacecraft that can scour the moon's surface before the US sends astronauts there around 2027.
