CAIRO, Dec 30 (Reuters) - Egypt's central bank said it was offering $75 million at its first foreign currency auction on Sunday, with a maximum $11 million per bank.

The auction is part of a new currency regime the bank announced on Saturday to conserve its foreign reserves, which it said have fallen to a critical level.

Under the regime, Egyptian banks will not be able to hold long positions in U.S. dollars of more than 1 percent of their capital, down from a previous 10 percent, corporate clients will be limited to daily cash withdrawals of $30,000 and individuals who purchase foreign currencies will be charged a 1-2 percent administrative fee, bankers said.