DUBAI, May 29 (Reuters) - Shares in Kuwaiti companies linked with the al-Kharafi family tumbled on Sunday after the multibillion-dollar sale of another Kharafi-controlled business was scrapped.

Investment company Adeptio had agreed in February to buy 69 percent of Kuwait Food Co (Americana) from Al Khair for Stocks and Real Estate, which is run by the wealthy Kharafi merchant family, but Al Khair announced on Sunday that the plans have been scrapped.

Americana's shares were suspended ahead of the market open and have yet to resume trading, but other Kharafi-linked stocks plunged.

National Industries Groupand National Investment Co slid 1.8 percent and 8.9 percent respectively, while Al Mal fell 6.2 percent. The Kharafis own stakes in all four of the companies, Thomson Reuters data shows.

Kuwait's index fell 0.6 percent to 5,362 points.

Elsewhere, Dubai Parks and Resorts hit a record peak to help to lift Dubai's index to a two-week high in otherwise subdued trading.

The company, which completed a 1.68 billion dirham ($457.44 million) rights issue last week, rose 4.2 percent to 1.49 dirhams. The stock accounted for two thirds of all shares traded on the benchmark index and took its gains to 17 percent in three sessions.

The Dubai index rose 0.3 percent to 3,360 points, reaching its highest level since May 12 and looked set for a fourth straight advance despite losers outnumbering gainers 10 to eight.

Volumes have slumped since late April, but the trend ahead of the Muslim holy month of Ramadan -- which starts in early June -- could yet be disturbed, said Marwan Shurrab, director at Vision Investments and Holding in Dubai.

Shurrab predicts that speculation over a possible rise in U.S. interest rates and a June referendum on whether Britain should leave the European Union will contribute to Dubai stock volatility before Ramadan.

Among Gulf bourses, Dubai tends to track international markets most closely because foreign investors have a bigger influence.

Saudi Arabia's benchmark fell 0.9 percent to 6,423 points, taking its losses to 6.5 percent since the 16-week high hit on April 25.

Saudi Basic Industries Corp , the Gulf's largest listed company, was the biggest faller with a 1.8 percent decline. ($1 = 3.6726 UAE dirham)

(Reporting by Matt Smith; Editing by David Goodman) ((celine.aswad@thomsonreuters.com; +971 4 4536886; Reuters Messaging: celine.aswad.thomsonreuters.com@reuters.net))