Anxiety about a political and economic crisis has gripped Egypt in recent weeks, with many people rushing to buy US dollars and withdraw savings.
The new constitution, which the liberal opposition says betrays Egypt's 2011 revolution by dangerously mixing religion and politics, has polarised the Arab world's most populous nation and prompted violent scenes.
The constitution text won about 64% of the vote in a public referendum, paving the way for a new parliamentary election in about two months.
The charter states the principles of sharia, Islamic law, are the main source of legislation and that Islamic authorities will be consulted on sharia.
This is a source of concern to the Christian minority and others.
Mr Mursi's government is preparing to impose austerity measures.
This week the Standard & Poor's agency downgraded Egypt's long-term credit rating.