Tesla has also been fined by officials in South Korea after a study found its cars were delivering just half their claimed range in cold weather conditions.
Like petrol cars, electric vehicles can lose mileage more quickly in colder conditions. They can also lose power when running their air conditioning or heating.
It comes as a further blow to Mr Musk, with US officials already scrutinising Tesla’s claims about its self-driving car technology. The US highways agency is also examining dozens of crashes involving Tesla’s Autopilot driver assistance tools.
In February, the US National Highway Traffic Safety Administration ordered Tesla to issue a software update to 363,000 vehicles running Tesla’s “full self-driving” system over concerns they may be ignoring stop signs and speed limits. Tesla said it disagreed with the findings but had made the update “out of an abundance of caution”.
US officials have also reportedly been probing the use of Tesla funds to build a glass house for Mr Musk in Texas and whether this had been properly disclosed to investors.
Of the latest investigations, Tesla said: “To our knowledge no government agency in any ongoing investigation has concluded that any wrongdoing occurred.”
Shares in Tesla fell 3.4pc in early trading in the US, although later recovered to trade flat at $212 (£173). The company’s shares are up 97pc so far this year despite concerns over waning demand for new EVs.
Electric car companies are facing increased scrutiny over their claims about range and recharging in advertising and marketing materials.
The UK’s Advertising Standards Authority banned two adverts from Hyundai and Toyota over exaggerated claims about recharging their electric cars. Both companies argued their adverts were not misleading.
Last week, Tesla reported revenues of $23.3bn, slightly below Wall Street expectations. Its profits came in at $1.85bn for the three months ending in September, lower than the previous quarter and down 44pc on the same period a year earlier.
The company has been trimming the prices of its electric vehicles to keep boosting sales amid stiff competition from new rivals, such as China’s BYD. Next month, Mr Musk plans to launch deliveries of a long-delayed pick-up, the Tesla Cybertruck.