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The Palo Alto, California-based carmaker saw deliveries bounce back by 69 percent compared to a rough first quarter in 2016. Tesla produced 25,418 vehicles, a bit above its prior record in the third quarter of 2016.
That puts Tesla on track to meet its target of 50,000 units in the first half of the year. In the first quarter it delivered 13,450 of the Model S and 11,550 of the larger Model X.
Its upcoming Model 3 is priced at a moderate $35,000 in the United States, far below the price of its initial Models S and X vehicles.
The Model 3 was designed from the outset to be more efficient to make, a move intended to avoid production stumbles.
CEO Elon Musk voiced confidence in February that Tesla electric car production would climb to 500,000 next year.
Tesla in January began mass production of energy-saving batteries that it vows will take electric cars mainstream.
A "Gigafactory" created by Tesla and Panasonic is cranking out lithium-ion battery cells, which will be used in Tesla's energy storage products and the Model 3, according to the carmaker's website.
The Gigafactory, located in the western state of Nevada, is also working on residential energy storage technology that could be used to power homes with solar energy.