Musk said that full details regarding the source of funding would be provided before anyone would be asked to decide on going private but that it was "premature" to share such information on Monday.
Investigators in the Securities and Exchange Commission's San Francisco office are also scrutinizing Musk's moves.
The first such suit was filed Friday by Tesla short seller Kalman Isaacs, who contended that the tweets were exclusively meant to manipulate the company's stock price - a move that's estimated to have cost Isaacs and those making similar bets upwards of $US1 billion ($1.4 billion). Musk justifies the Saudi interest in electric vehicles and his company with their need to "diversify away from oil".
The committee has the authority to evaluate and negotiate a potential deal, or any alternatives proposed by Mr. Musk, on the board's behalf, Tesla said.
Tesla declined to comment further on the matter.
Musk's tweet caused a financial firestorm with Tesla shares immediately skyrocketing by nearly 11 percent, although in the coming days they lost a good part of what they had gained. Tesla bought SolarCity that year. Buss is the former CFO of Solar City before Tesla's somewhat controversial buyout of the company, Denholm is the first female member of Tesla's board of directors, and Rice is the second.
The SEC is looking into whether Musk's initial announcement broke a rule preventing public companies from announcing such major financial plans if they don't intend to see them through, don't have financing secured, or are blatantly trying to manipulate the stock price.
Tesla's other board members include Musk; his brother Kimbal Musk; Twenty-First Century Fox's CEO James Murdoch; Antonio Gracias, founder of Valor Equity Partners; and Ira Ehrenpreis, founder of venture capital firm DBL Partners. The company has separately retained Wilson Sonsini Goodrich & Rosati for legal counsel.