CAIRO, Aug 28 (Reuters) - The Egyptian pound strengthened on both the official and black markets on Wednesday as concerns the country faced sustained instability eased further, traders said.

The black market has been dwindling since the army deposed Islamist President Mohamed Mursi on July 3 and the subsequent arrival of $5 billion of aid from Gulf Arab states to top up the country's foreign reserves.

The central bank sold $38.8 million and the cut-off price was 6.9760 Egyptian pounds per dollar versus 6.9764 at a sale on Monday, the bank said. The bank had offered $40 million.

Black market dealers were offering to buy dollars for about 7.10 Egyptian pounds on Wednesday and sell them for 7.14 pounds compared to 7.15 and 7.20 pounds on Monday, currency traders said.

The black market rate had weakened to 7.20 and 7.25 on Thursday ahead of anti-army protests called for the following day but regained strength this week after the protests failed to attract large crowds.

The pound weakened on the black market early this year to as low as 8.05 per dollar as the country drained foreign reserves - already low following a plunge in foreign investment and tourism due to turmoil since the country's popular uprising in early 2011 - to support the currency.

The $5 billion in Gulf aid has helped the central bank to support the pound and the pound's official price, controlled by the central bank, has been appreciating slowly since Mursi's overthrow.

The central bank introduced currency sales, held three times a week, at the end of December to help to stave off a currency crisis and 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. (Reporting by Patrick Werr; Editing by Toby Chopra)