CAIRO, Sept 11 (Reuters) - Egypt's pound strengthened marginally at a central bank foreign currency sale on Wednesday.

The central bank sold $38.8 million with a cut-off price of 6.8853 Egyptian pounds per dollar versus 6.8855 pounds at its last sale on Monday, the bank said. It had offered $40 million.

Last Wednesday, the pound jumped 1.2 percent to 6.8952 pounds to the dollar at a special $1.3-billion foreign currency sale - its biggest ever.

The pound weakened on the black market early this year as far as 8.05 per dollar after foreign reserves were drained by a plunge in foreign investment and tourism since the country's popular uprising in early 2011.

The black market has shrunk since the army deposed President Mohamed Mursi on July 3.

The central bank introduced currency sales, held three times a week, at the end of December to help to thwart a run on the pound.

Since Mursi was ousted, the central bank has allowed its official cut-off price to appreciate gradually from a low of 7.0184 on July 3.

More than 2,000 Islamist activists have been arrested since Mursi was ousted and more than 1,000 people have been killed in political violence. (Reporting by Shadia Nasralla; Editing by Stephen Nisbet)