(Reuters) - Egypt's central bank kept the pound steady at 8.78 pounds to the dollar at an official foreign currency auction on Tuesday, its first sale of foreign currency since raising its benchmark interest rate by one percentage point last week.

Central bank data showed it had sold $115.6 million at a cut-off price of 8.78 pounds per dollar, unchanged from last week. The currency was weaker on the black market.

Currency traders cited a range of 11.05-11.08 pounds per dollar as the black market rate on Tuesday, slightly weaker than last week's rate of 10.95 pounds per dollar.

Egypt's central bank has permanently closed two more exchange companies for selling foreign currency at more than the official rate as it steps up a campaign to crush a flourishing black market, exchange bureau and central bank sources said.

The central bank has been cracking down on exchange bureaux trading dollars at a rate far outside its set range but the gap between official and black market rates continues to widen and a March devaluation failed to ease an acute dollar shortage.

Dollars are rationed through weekly auctions, giving priority for imports of essential goods.

The central bank has kept the pound artificially strong since it devalued the currency in March to 8.78 per dollar from 7.7301 and announced a more flexible exchange rate policy.

Last Thursday, the Monetary Policy Committee (MPC) raised the overnight deposit rate from 10.75 percent to 11.75 percent, its highest in over a decade. It hiked the overnight lending rate from 11.75 percent to 12.75 percent, its highest since 2008.

A shortage of dollars in the formal banking system since a 2011 uprising that drove away tourists and foreign investors, key sources of hard currency, has made it difficult for import businesses. Many of them now rely on a black market where they can procure currency for a higher price.

The pound's rate on the black market has grown weaker since the March devaluation, at which time it was roughly in line with the official rate.

(Reporting by Ola Noureldin; Editing by Catherine Evans)