Tesla's Model Y robotaxi finally hit the road this weekend, sending shares of the electric vehicle maker up 9% on Monday.

The EV giant debuted autonomous rides in Austin, Texas, on Sunday, opening the service to a limited number of riders by invitation only.

Those invited included longtime Tesla fans, promoters and shareholders, many of whom generate income from posting Tesla- and Musk-related social media content on platforms including X and YouTube.

CEO Elon Musk said in a post on his social network X that customers were charged a flat fee of $4.20 per ride.

"Super congratulations to the @Tesla_AI software & chip design teams on a successful @Robotaxi launch!! Culmination of a decade of hard work. Both the AI chip and software teams were built from scratch within Tesla," he said in a post.

One passenger in Tesla's early access program for the Model Y robotaxis wrote on X that they did 11 rides with the service with "zero issues." Musk reposted numerous firsthand encounters with the services.

Other road users and researchers observed the robotaxis appearing to violate traffic rules in Austin.

The Verge reported a Tesla Model Y robotaxi briefly traveled the wrong way down a road in Austin. Tesla-critical author Ed Niedermeyer shared a video from Austin showing a Tesla robotaxi braking hard in the middle of traffic in response to "stationary police vehicles outside its driving path."

Musk has long promised a Tesla robotaxi fleet to investors, amping up the pressure to deliver in recent months.

Once considered a pioneer, Tesla is now trying to catch up to Alphabet's Waymo in the West, and Chinese competitors including Baidu's Apollo Go, WeRide and Pony.ai. Waymo has reported that it is now delivering more than 250,000 commercial driverless rides per week and surpassed 10 million trips last month. Apollo Go reported that it has surpassed 11 million trips.

Musk told CNBC's David Faber last month that Tesla aims to have "hundreds of thousands, if not over a million" self-driving cars in the U.S. by the end of next year. In May, Musk first announced plans to launch the service in Austin, with later debuts set for Los Angeles and San Francisco.

Heading into the launch, Tesla faced pushback from a group of Democratic lawmakers in Texas and public safety advocates who urged the company to delay the debut.

The company has not yet released the systems being tested on Texas streets, known as FSD Unsupervised, to general Tesla owners.

Tesla sells its new EVs with partially automated driving systems marketed as the standard Autopilot, and premium FSD Supervised systems. These include features such as automatic lane-keeping and navigation, and have been linked to accidents, including fatalities, according to data tracked by the National Highway Traffic Safety Administration.

— CNBC's Lora Kolodny contributed reporting.