Anxiety about a deepening political and economic crisis has gripped Egypt in past weeks, with many people rushing to buy dollars and withdraw their savings from banks.
The Egyptian pound tumbled to its weakest level against the U.S. currency in almost eight years.
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 occasionally violent protest on the streets.
In his first address to the nation of 84 million since the adoption of the new constitution, Mursi said it was time for all political forces to put aside their differences and start working together to bring stability.
"I will make all efforts, together with you, to push forward the economy which faces huge challenges and has great opportunities to grow," Mursi said in a televised speech.
The presidency announced on Wednesday (local time) that he had formally approved the constitution the previous evening, shortly after results showed that Egyptians had backed it in a referendum.
The text won about 64 percent of the vote, paving the way for a new parliamentary election in about two months.
The charter states that the principles of sharia, Islamic law, are the main source of legislation and that Islamic authorities will be consulted on sharia - a source of concern to the Christian minority and others.
The referendum result marked yet another electoral victory for the Islamists since veteran autocrat Hosni Mubarak was toppled in 2011, following parliamentary elections last year and the presidential vote that brought Mursi to power this year.
Mursi's government, which has accused opponents of damaging the economy by prolonging political upheaval, now faces the tough task of building a broad consensus as it prepares to impose austerity measures.
In his speech, Mursi said he would introduce incentives to make Egypt a more attractive place for investors and considered making changes in the cabinet as part of his plan.
"The coming days will witness, God willing, the launch of new projects ... and a package of incentives for investors to support the Egyptian market and the economy," he said.
The atmosphere of crisis deepened this week after the Standard & Poor's agency downgraded Egypt's long-term credit rating and warned of a possible further cut. The government has imposed currency restrictions to reduce capital flight.
The pound traded as low as 6.1775 against the dollar on Wednesday, close to its all-time low of 6.26 hit on Oct. 14, 2004, on concerns that the government might devalue or tighten restrictions on currency movements.
"All customers are rushing to buy dollars after the downgrading," said a dealer at a Cairo-based bank. "We'll have to wait to see how the market will operate with the U.S. dollar, because as you know there is a rush at the moment."
Keen to be seen as decisive, the government is now in talks with business figures, trade unions and other groups to highlight the need for tax increases to resolve the crisis.
Mursi has committed to such austerity measures to receive a $4.8 billion loan from the International Monetary Fund.
However, Al-Mal newspaper quoted Planning Minister Ashraf al-Araby as saying the government would not implement the tax increases until it had completed the dialogue with different parts of society.
In Cairo's bustling centre, people openly expressed their frustration with economic instability as they went about their daily business.
"The country's going to the pits. Everything is a mess," Hamdy Hussein, a 61-year-old building janitor, said angrily. "It's worse than ever. Mubarak was better than now. People were living and there was security."
Ashraf Mohamed Kamal, 30, added: "The economic situation will be a mess in the next few years. It already is. People will get hungrier. People are now begging more."
Mursi, catapulted into power by his Islamist allies this year, believes adopting the constitution quickly and holding the vote for a permanent new parliament will help to end the long period of turmoil and uncertainty that has wrecked the economy.
Mursi's government argues the constitution offers enough protection to all groups, and that many Egyptians are fed up with street protests that have prevented a return to normality and distracted the government from tackling the economy.
The charter gives Egypt's upper house of parliament, which is dominated by Islamists, full legislative powers until the vote for a new lower house is held.
While stressing the importance of political stability to heal the economy, Mursi's government has tried to play down the economic problems and appealed for unity despite the hardship.
"The government calls on the people not to worry about the country's economy," Parliamentary Affairs Minister Mohamed Mahsoub told the upper house in a speech. "We are not facing an economic problem but a political one and it is affecting the economic situation. We therefore urge all groups, opponents and brothers, to achieve wide reconciliation and consensus."
Mursi is due to address the upper house on Saturday in a speech likely to be dominated by economic policy.
Sharpening people's concerns, the authorities imposed currency controls on Tuesday to prevent capital flight. Leaving or entering Egypt with more than $10,000 in cash is now banned.
Adding to the government's long list of worries, Communications Minister Hany Mahmoud has resigned citing his "inability to adapt to the government's working culture".
The opposition has condemned the new basic law as too Islamist, saying it could allow clerics to intervene in the lawmaking process and leave minority groups without proper legal protection. It said this month's vote was marred by major violations.
Nevertheless, major opposition groups have not called for new protests, suggesting that weeks of civil unrest over the constitution may be subsiding now that it has passed.
The United States, which provides $1.3 billion a year in military aid plus other support to Egypt and sees it as a pillar of security in the Middle East, called on Egyptian politicians to bridge divisions and on all sides to reject violence.