Tesla began limited operations of a self-driving taxi service Sunday in Austin, Texas, the first step in a rollout that Elon Musk, the company’s chief executive, has said will make autonomous ride-hailing ubiquitous while bringing in hundreds of billions of dollars of revenue.

At its start, the service, which Tesla calls Robotaxi, was available only to select guests, and the vehicles were confined to certain streets. Safety monitors rode in the front passenger seats, and the vehicles may not operate in bad weather, Tesla told people who received invitations to use the service.

“As an Early Access rider, you will be among the first to use our new Robotaxi app and experience an autonomous ride within our geofenced area in Austin,” read an invitation posted on X Friday by Sawyer Merritt, a Tesla investor who comments frequently on the company.

Tesla’s $1 trillion stock market valuation rests largely on promises by Mr. Musk that the company will be able to use artificial intelligence to allow its electric cars to drive autonomously pretty much anywhere there are roads. The Austin project has attracted feverish attention from investors, analysts and supporters of Tesla. The limited rollout will provide the first indications of whether Tesla’s technology can match Mr. Musk’s ambitions.

Tesla still has a long way to go, some analysts said.

“So far, this launch lags significantly behind the company’s promise and what competitors have already delivered,” Paul Miller, a principal analyst at Forrester Research, said in a statement.

Several of the people invited to test the Robotaxis, most of whom seemed to be Tesla enthusiasts with large presences on social media, posted videos of the experience on Sunday. Herbert Ong, who posts about Tesla regularly on X, had to walk several blocks to rendezvous with a Robotaxi after summoning it from a Tesla app.