Sisi, who toppled Egypt's first freely elected leader last July following mass protests, is joining a long line of leaders drawn from the military and enjoys the backing of wealthy Gulf Arab states. Black market traders have cited hopes of new investment and aid from Gulf countries as a reason why demand for hard currency had weakened.
On the black market, the dollar changed hands at a rate of 7.25/27 on Monday, in line with last week's rate. Narrowing the gap between official and unofficial rates, the pound has strengthened markedly in the black market since Sisi was elected on May 29.
It had traded for around 7.50 to the dollar before his election victory.
The central bank said it sold $37.6 million at a cut-off price of 7.1402 pounds, inching up from 7.1403 at its last sale on Thursday. It had offered $40 million.
Business leaders have cited clarity on the direction of the currency as a condition for further investment.
Egypt's central bank governor Hisham Ramez was quoted by state media on Saturday as saying that the bank's forex policies were succeeding in restoring stability to the currency market and would lead to the elimination of the black market.
Forex traders and economists have described the central bank's decision to allow the pound to gradually weaken since March as a managed depreciation.
The central bank has not said why it has been letting the currency weaken.
The rates at which banks are allowed to trade dollars are determined by the results of the central bank sales, giving the bank effective control over official exchange rates.
Egypt's foreign reserves fell to $17.284 billion at the end of May from $17.489 billion in April, the central bank said on Thursday. It had sold $1.1 billion at an exceptional forex auction on May 14.
May's dollar reserves compared with a cushion of over $35 billion in reserves before the 2011 uprising that swept veteran autocrat Hosni Mubarak from power and started three years of political turmoil that unnerved tourists and investors, two main sources of dollar inflows.