Egypt's central bank said it was offering to sell US$75 million to banks on Monday at its second foreign currency auction, with a maximum of $11 million per bank.
The auctions are part of a shift in currency policy announced on Saturday and designed to conserve the country's foreign reserves, which the bank says are critically low.
The bank also offered $75 million at its maiden auction on Sunday.
It accepted bids worth $74.9 million, with a cut-off price for dollars of 6.2425 Egyptian pounds. This represented a substantial weakening of the pound, which was earlier bid in the interbank market on Sunday at 6.185 to the dollar.
The Egyptian pound fell on the interbank market to a record low of about 6.30 to the US dollar after Sunday's auctions.
Political turmoil over a new Constitution has sent worried Egyptians scrambling to turn their savings into dollars. The central bank said on Saturday that foreign reserves were now at a critical level and could barely cover three months of imports.
The changes announced on Saturday include regular foreign currency auctions and commercial bank officials say they point to an orderly devaluation of the pound after the central bank spent more than $20 billion - or more than half of its reserves - over the past two years to defend the currency.
The currency crisis underlines the scale of the economic challenge facing President Morsy, who has been grappling with the fall-out of a political crisis ignited by his move to drive through a Constitution written by his Islamist allies.