Still scrambling to sort out production problems at its electric car factory in California, Tesla is taking on another challenge: building a new plant and development center in China.

The automaker said Tuesday it reached an agreement with Chinese authorities to build a battery and automobile factory in Shanghai — its first plant outside the United States — that would be capable of producing 500,000 electric vehicles a year.

The company did not disclose how much it planned to invest, but said Tesla would be the sole owner. Other automakers have been required to form joint ventures with local partners to produce cars in China. The Chinese government said it would ease that requirement.

Tesla said it expected to begin construction once it obtained approvals and permits.

“From there, it will take roughly two years until we start producing vehicles and then another two to three years before the factory is fully ramped up,” the company said in a statement.

Setting up a plant in China will not be easy, and one of the toughest parts may be finding executives to manage the effort, said Ron Harbour, an auto-manufacturing expert at Oliver Wyman, a consulting firm.

“They are trying to get going in California, so who are they going to send overseas to do the same thing?” he said. “You usually want to get it right at home first.”

The investment in China is the latest initiative Tesla’s chief executive, Elon Musk, announced with lofty ambitions.

Two years ago, Musk predicted the company’s plant in Fremont, California, would churn out 500,000 cars by this year, but by the end of June, about 40,000 were in transit or delivered.

Tesla began selling cars in China in 2013 and set up 35 sales centers and some 1,200 charging stations in the country. It sold about 15,000 cars there last year, according to estimates by LMC Automotive.