Tesla's China-made electric vehicle sales fell 9.9% to 61,497 units in October from a year earlier, reversing a 2.8% increase in September, data from the China Passenger Car Association showed on Tuesday.

Sales of the U.S. automaker's Model 3 and Model Y vehicles made at its Shanghai "gigafactory", including exports to Europe, India and other markets, dropped 32.3% from September.

Its biggest Chinese rival, BYD, posted a 12% drop in global vehicle sales last month, a second consecutive month of decline and the steepest fall in nearly two years amid hyper-competition in the home market.

Tesla has not yet announced the availability on the Chinese market of the lower-cost versions of its best-selling Model Y SUVs and Model 3 sedans, which were unveiled last month.

In spite of the swift European roll-out of the new cars, which opt out of some premium features, Tesla sales resumed falling in a number of countries there, pointing to continued struggles on a continent that has been crowded with budget EVs.

By comparison, BYD has seen robust sales growth in Europe even while its growth on home turf hit a speed bump.

Tesla is also set to showcase its Cybercab in Shanghai from Wednesday. It remains unknown if Tesla has planned the robotaxi's roll-out on Chinese roads where local firms such as Baidu, Pony.ai and WeRide have been testing their robotaxis in various cities.