By Stephen Kalin

CAIRO, July 2 (Reuters) - The central bank let the Egyptian pound depreciate for the first time in five months on Thursday, a move analysts said would please the international investors that Cairo is courting.

The bank said it sold $38.8 million at a cutoff price of 7.63 pounds per dollar at a regular auction, sending the currency to its weakest level since auctions began in December 2012.

The new rate is 1.3 percent weaker than the rate of 7.53 pounds at the previous auction on Sunday.

Letting the pound weaken in a controlled manner again after doing so over a few weeks earlier this year could boost exports and attract further investment, analysts said.

At the same time, a weaker currency could raise Egypt's large bill for imports, which many Egyptians rely on for fuel and food staples.

Egypt is trying to rebuild its economy after four years of turmoil with a series of investor-friendly reforms including reducing subsidies and introducing pro-business regulations.

But hopes of a quick turnaround have been hit by continuing violence.

And questions remain over the availability of foreign currency, even as some investors signed billions of dollars worth of deals at an investment summit in March.

"We have a problem with availability of dollars so we need to have a weaker currency to attract capital," said Mohamed Abu Basha, economist at EFG-Hermes in Cairo.

MANAGED FLEXIBILITY

The central bank began auctioning dollars in December 2012, which bankers saw as a possible controlled shift towards a free float. But two years later the central bank still plays a powerful role in supporting the pound.

The rates at which banks are allowed to trade dollars are determined by the results of central bank sales, giving the bank effective control over official exchange rates.

"It would make sense to show managed currency flexibility rather than holding onto the natural attitude of a strong currency," Angus Blair, chairman of business and economic forecasting think-tank Signet, told Reuters.

He said the timing could be related to the approval of a new budget on Wednesday, which cut the projected deficit to 8.9 percent of gross domestic product.

There was no official statement from the central bank.

As well as letting the pound depreciate, Egypt has taken steps to eliminate a once-thriving currency black market, including capping dollar-denominated bank deposits.

Local currency traders said the pound was changing hands at 7.68 pounds, unchanged from the rate following the previous auction on Sunday.

But one trader said the rate on the parallel market was at 7.77 pounds, and another quoted 7.80, outside the 0.15-pound band set by the central bank.

The central bank gave banks permission in January to trade dollars up to 0.10 pounds more or less than the official rate, with an extra 0.05 pounds for currency exchange bureaus. (Additional reporting by Ahmed Aboulenein)