The election of Morsi, 60, chairman of the Islamic Brotherhood's Freedom and Justice Party, has fed fears among Christians and more liberal Muslims that the Islamists will use their political mandate to impose conservative restrictions on dress and behavior.
A statement to Morsi from the Coptic Catholic Church June 25 praised his apparent "willingness ... to work with skilled people of all groups and sectors of society to achieve the common good."
"We pray that the Lord gives you success ... in developing the institutions necessary for the realization of a modern democratic civil state -- a state that respects the rights and freedoms of everyone and guarantees security, peace and social justice."
The June 24 declaration of Morsi as the winner of the June 16-17 vote followed a week of uncertainty in which Egypt's military ruling council introduced constitutional amendments that stripped the presidency of most of its powers and disbanded Parliament, giving the generals legislative authority and oversight in the drafting of the constitution. The military police also were granted broad powers to detain civilians.
The military council promised to turn over power to the new president by June 30.
Prior to the election announcement, Coptic Bishop Kyrillos William of Assiut, Egypt, told Catholic News Service he did not think Morsi "will have so much authority."
"The army's moves mean he doesn't have a constitution or Parliament to help him," the bishop said.
"From the beginning the army promised a civil state. It was essentially a guarantee," he added.
Shafiq's avowed secularism and pledge to use a firm hand to restore security had won him the backing of many Christian voters. He also was the military council's preferred candidate.
For his part, Morsi promised a "civil, democratic, constitutional and modern state." He has said his administration will include women and minorities in key positions, pledges met with skepticism by many Christians.
"It's our tough luck to have Morsi for four years to come," said Amgad Wahby, 35, standing outside of the Catholic basilica in Cairo.
"(The brotherhood) have to change their priorities in order to survive. They need to try to be lenient at the beginning, but in the future they will probably try to return to their old, autocratic style," he said.
But Wahby said any attempt to restrict religious and human rights would be met with "friction."
Father Rafic Grieche, spokesman for the Egyptian bishops' conference, noted that Egypt's Christians had lived under Islamic regimes for 1,400 years.
"We hope Morsi will be a just ruler," said Father Grieche. "Mubarak's time was not fair, and I do not think Morsi could be worse.
"At the same time, the people of Islamic tendencies will be working to Islamicize the society. You don't need laws to do this. It can happen in day-to-day life," he said, explaining, for example, that an employer might opt to hire a woman wearing a veil rather than one who did not.
One young woman placed her trust in God.
"I'm disappointed, but I am not afraid. God is there to protect us, life will go on," said Farah, a 17-year old worshipper at the June 25 Melkite Catholic Mass. "If the worst happens and they try to make changes, then we will object. We will start another revolution. We won't just give up."