Xpeng, the Chinese electric vehicle start-up often cast as a key rival to Tesla, has set an ambitious goal to surpass the US carmaker’s self-driving capabilities in China by August, according to co-founder, chairman and CEO He Xiaopeng.

The target highlights an intensifying technology race in the world’s largest car market, where manufacturers are increasingly leaning on advanced software to drive growth as government subsidies are phased out.

Although Tesla’s full version of its Full...