Elon Musk, the chief executive of Tesla, tried for years to persuade Chinese regulators to let him offer self-driving capabilities in one of the company’s most important markets.

       After a series of false starts, Mr. Musk is now closer than ever.

       Tesla said on Tuesday that some drivers in China would be able to use the company’s Autopilot feature on city streets to help with lane changes and other more advanced tasks. Cars that use the update, which is similar Tesla’s Autopilot feature in the United States, are not completely autonomous and still require supervision from the driver. The update is available to Tesla owners who paid an extra $8,800.

       The news marked a breakthrough for Mr. Musk in China, where his company has faced increasingly tough competition. It is an important step toward Mr. Musk’s goal of offering full self-driving in China, something that would help Tesla to claw back some of the market share it has lost in recent years.

       Mr. Musk has identified autonomous-driving technology as critical to Tesla’s future. The company has fallen behind in China, where regulators have been slow to approve its latest self-driving functions. Days after stressing the importance of the technology to investors last year, Mr. Musk traveled to Beijing to meet with China’s No. 2 official, Li Qiang. Not long after, Tesla was among a group of Chinese automakers to receive approval for their data security precautions on some models.

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       Mr. Musk has since ascended to a position of power in the U.S. government as an aide to President Trump, who is sparring with China over trade policy.

       Getting approval for its most advanced self-driving technology would help “give Tesla three to five more years of technology leadership in China’s hypercompetitive electric vehicle market,” said Michael Dunne, an auto consultant and former General Motors executive.

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