CAIRO, June 3 (Reuters) - Egypt's central bank sold $38.8 million to banks in a foreign exchange auction on Monday, with the cut-off price little changed at 6.9753 Egyptian pounds to the dollar.

The cut-off price at Thursday's auction was 6.9738 pounds.

The central bank has slowed the speed of the pound's weakening over the last two weeks, and currency dealers say it seems reluctant to allow it to weaken below the psychologically important mark of 7.00 to the dollar.

On the black market, one dealer was offering to buy dollars on Monday for 7.35 pounds and to sell dollars for 7.40 pounds.

The central bank introduced the auctions at the end of December to help stave off a currency crisis and thwart a run on the pound. Since then, it has let the currency weaken by more than 11 percent against the dollar on the official market.