DUBAI (Reuters) -Saudi Arabia's sale of shares in oil giant Aramco drew more demand than the stock on offer within hours of kicking off on Sunday, a landmark deal that could raise up to $13.1 billion in a major test of international appetite for the kingdom's assets.

The banks on the deal will take institutional orders through Thursday and will price the shares the following day, with trading expected to start next Sunday on Riyadh's Saudi Exchange.

The offering will be a gauge of Riyadh's appeal to foreign investors, a key plank of the kingdom's ambitious plan to overhaul its economy. Foreign direct investment has repeatedly missed its targets.

The sale will also bolster efforts by the government to wean itself off its "oil addiction", as Saudi de facto ruler Crown Prince Mohammed bin Salman once called it, analysts and sources have said.

The sovereign wealth fund, the Public Investment Fund (PIF), the preferred vehicle driving the mammoth agenda that has poured tens of billions of dollars into everything from sports to futuristic desert cities, is likely to be a beneficiary of the funds, they said.

Aramco's shares were down 2.6% on Sunday to 28.25 riyals ($7.53) as of 0825 GMT.

Saudi Arabia is offering investors about 1.545 billion Aramco shares, or 0.64%, at 26.7 to 29 riyals, or just under $12 billion at the top end of the range.

"Books are covered on the full deal size within the price range," meaning indicated demand exceeded deal size, one of the banks on the deal said,.

The banks can increase the offering by a further roughly $1 billion. If all the shares are sold, the Saudi government will be cutting its stake in the world's top oil exporter by 0.7%.

The world's top investment banks are helping to manage the sale - Citi, Goldman Sachs, HSBC, JPMorgan, Bank of America and Morgan Stanley - along with local firms Saudi National Bank, Al Rajhi Capital, Riyad Capital and Saudi Fransi.

M. Klein and Company and Moelis are independent financial advisers for the deal.

UBS Group's Credit Suisse Saudi Arabia unit alongside BNP Paribas, Bank of China International and China International Capital Corporation are also helping to seek buyers for the shares, according to a stock exchange filing on Sunday.

About 10% of the new offering will be reserved for retail investors, subject to demand.

The deal kicks off as the OPEC+ group of oil producers is set to meet on Sunday to determine output policy, with some ministers meeting in Riyadh, according to OPEC+ sources.

The de facto Saudi-led Organization of the Petroleum Exporting Countries and allies led by Russia, together known as OPEC+, is currently cutting output by a total of 5.86 million barrels per day (mbpd), equal to about 5.7% of global demand.

Still, Aramco - long a cash cow for the Saudi state - has boosted its dividends, introducing a new performance-linked payout mechanism last year, despite lower profits as a result of the lower volumes. Saudi Arabia is producing about 9 mbpd of crude, roughly 75% of its maximum capacity.

The Saudi government directly holds just over 82% of Aramco. PIF owns 16% - 12% directly and 4% through subsidiary Sanabil, with the remainder held by public investors.

($1 = 3.7507 riyals)