OSLO (Reuters) - Rules governing Norway's $1 trillion (£784 billion) wealth fund would allow it to stay on as an investor in Tesla if the electric carmaker goes private, its deputy CEO said on Tuesday.

Tesla CEO Elon Musk stunned financial markets this month when he revealed on Twitter he was considering a $420 per share take-private deal for the money-losing carmaker.

Norway is Tesla's third-biggest market and the country's wealth fund, the world's biggest sovereign wealth fund, had a 0.48 percent stake in Tesla worth about $253 million (£198.4 million) as of the start of 2018, according to the latest data from the fund.

Tesla shares have been hit by investor concerns about Musk's plan, and doubts about whether the company has secured the funding to go private, and the SEC has opened an inquiry related to Musk's tweets, according to a person with direct knowledge of the matter.

Trond Grande, deputy CEO of the Norwegian fund, declined to say whether Tesla had approached the fund about going private.

However, he said that although the fund's main practice is to sell its stake when a company leaves an exchange, or soon after, rules regulating the fund set by the Norwegian Finance Ministry and parliament do allow it to stay on in a listed company that goes private.

"The priority is to try to preserve the value for the fund. That is the priority," Grande told Reuters on the sidelines of an earnings presentation. "If that means that the fund will be invested in a company that has been delisted for a period of time, that could happen."

"But as a main rule, we will exit the investments as and when, or soon after, it has been taken off an exchange," he said.

CRITICAL OF TESLA

This year the fund has been critical of Tesla's approach on several issues.

In March it voted against Musk's potential $2.6 billion payout. Then in June it backed an initiative to wrest the role of chairman away from CEO Musk, and another that would have allowed investors to nominate their own directors.

Grande declined to speak specifically about the situation at Tesla. Generally speaking, he said the fund sees the importance of separating the roles of CEO and chairman and to allow independent directors on boards.

"We acknowledge some companies do not operate ... in that sense, but we will not change our stance with regards to that," he said.

The fund owns 1.4 percent of all globally listed shares. It invests in stocks, bonds and real estate worldwide.

In the second quarter, the fund made a return of 1.8 percent, it said on Tuesday, helped by a rise in global equity markets, although it still underperformed the index it is benchmarked against.

"North American and European stocks had a positive development in the quarter despite the prospect of increased trade barriers," Grande told a news conference.

The fund returned 0.2 percentage points less than a benchmark index set by the Norwegian Finance Ministry.

(Reporting by Gwladys Fouche, editing by Ole Petter Skonnord and Susan Fenton)

By Gwladys Fouche