SAN FRANCISCO/DETROIT (Reuters) - A group of Tesla Inc TSLA.O investors has urged the luxury electric car maker to add two new independent directors to its board, without ties to Chief Executive Elon Musk, to "provide a critical check on possible dysfunctional group dynamics."

A defiant Musk took to Twitter on Wednesday afternoon to suggest the investors buy stock in Ford Motor Co F.N instead. The Ford family controls the Detroit automaker through two classes of stock.

In a letter dated Monday, five investment groups including the California State Teachers Retirement System, Hermes Equity Ownership Services and CtW Investment Group urged Tesla to have all of its directors re-elected annually.

“We expect that as companies make the transition to publicly-traded status, the governance structures and practices in place at the time of the IPO will evolve to align with the company’s changing strategy,” the letter reads. “However, Tesla’s seven-member board is largely unchanged from its pre-IPO days.”

Led by the enigmatic Musk, Tesla recently became the most valuable U.S. car company, passing General Motors Co GM.N for the top spot.

Tesla’s market value has since slipped to just shy of GM’s. As of Wednesday, the market cap of the Silicon Valley automaker was $50.3 billion, while GM’s was $50.8 billion.

“This investor group should buy Ford stock,” Musk posted on Twitter on Wednesday afternoon. “Their governance is amazing...”

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Musk then said on Twitter that he would follow up soon on an earlier promise to appoint more independent directors, “but this (investor) group has nothing to do with it.”

Over the past month, Tesla stock has surged 35 percent as investors bet that Musk will revolutionize the automobile and energy industries. The shares closed down 3.8 percent at $296.84 in Wednesday’s trading on Nasdaq, however.

Among those on Tesla’s board is Kimbal Musk, the CEO’s brother, and Brad Buss, who served as chief financial officer at SolarCity Corp, which the electric car maker acquired last year.

The $2 billion stock deal for the money-losing installer of residential solar power systems, prompted a 13 percent fall in Tesla’s share price after Musk outlined it last June.

The Palo Alto, California-based company is rushing to launch its mass-market Model 3 sedan in the second half of this year and quickly ramp up its factory to hit a production target of 500,000 cars per year in 2018.

Last year Tesla sold 76,230 vehicles, missing its target of at least 80,000 cars sold. By comparison, GM sold 10 million cars and Ford sold 6.7 million.