The setback comes at a time when Tesla is under scrutiny from authorities over the safety of its semi-autonomous driving technology, which it calls "FSD."
Tesla did not immediately respond to requests for comment outside of regular U.S. business hours.
The launch of the new driving assistance system for some Tesla model owners, which the company says features several improvements, had been announced for Friday, Oct. 22.
On Saturday, Musk said the launch would likely be delayed by a day.
Tesla vehicles with the latest 10.3 software repeatedly issued forward collision warnings when there was no immediate danger, according to videos posted by beta users. Some vehicles also braked automatically for no reason, users said in social media posts.
Some users said they had lost the beta FSD software altogether after having problems with the latest version.
There was no information Sunday about a possible new release date, either from Musk on social media or from Tesla.
The National Highway Traffic Safety Administration (NHTSA) in August opened a formal investigation into the safety of Tesla's Autopilot system in 765,000 U.S. vehicles after a series of accidents involving Tesla models and emergency vehicles.