|United airlines glitch|
The airline, one of the largest in the US, said it was unsure how many steeply discounted tickets it had issued.
It temporarily shut down its website and ceased taking telephone orders after discovering the error.
The tickets were sold on Thursday through its online booking system. Passengers must still pay US security fees of about $5 (£3.15) - $10.
"We've reviewed the error that occurred yesterday and based on these specific circumstances, we will honor the tickets," the airline wrote in a tweet.
US travellers snatched up tickets for destinations as far afield as Hawaii.
Bob Stokas of Oak Lawn, a suburb of Chicago, told a local NBC affiliate he had been shopping for a return fare to Los Angeles, expecting to pay as much as $800.
"When I scrolled down past the non-stop fares, when I got to the connecting flights, the flights to and from Los Angeles per person was $10," he told the broadcaster.
"That was a shock and a surprise, and I was like, 'I've got to book this flight right now before they rescind their offer of $10 for this flight.'"