GWEN IFILL: Egypt has a new president, one whose election could represent a sharp turn from the Mubarak era.
Jeffrey Brown has the story.
JEFFREY BROWN: It was a remarkable moment, as thunderous cheers filled Cairo's Tahrir Square on Sunday and thousands of supporters of the Muslim Brotherhood, a party that had been officially outlawed for decades, celebrated the election of one of their own, Mohammed Morsi, as president of Egypt.
MOHAMED AL GIZAWI, Morsi supporter (through translator): Thank God for the results. The revolution has succeeded. The revolution continues.
JEFFREY BROWN: Sixty-year-old Morsi is an American-educated engineer. He won just under 52 percent of the vote in a runoff with Ahmed Shafiq, who served as the last prime minister under ousted President Hosni Mubarak.
Speaking on television last night, Morsi promised to be president of all Egyptians.
MOHAMMED MORSI, Egyptian President-Elect (through translator): I'm determined with you to build a new Egypt, a national state with a modern democratic constitution. And I will spend all my time on this big project.
JEFFREY BROWN: The new president-elect becomes the first Islamist to head the Egyptian state and the first civilian to hold the office. Last night, he also addressed concerns about Egypt's international agreements, including with Israel.
MOHAMMED MORSI (through translator): We will preserve the international accords and treaties. We carry a message of peace to the world.
JEFFREY BROWN: An Israeli Foreign Ministry spokesman welcomed the news.
YIGAL PALMOR, Spokesman, Israeli Foreign Ministry: We have the greatest respect for democratic choice by the people. And we look forward to continuing the cooperation with the Egyptian government and the Egyptian administration on the basis of the Israel-Egypt peace -- peace agreement, which is a joint interest of both countries.
JUDY WOODRUFF: In Washington today, the State Department's Victoria Nuland said much more remains to be done in Egypt.
VICTORIA NULAND, State Department Spokeswoman: We want to see president-elect Morsi take steps to advance national unity, to uphold universal values, to respect the rights of all Egyptians, particularly women, minorities, Christians, et cetera.
JEFFREY BROWN: In fact, as Morsi met today with Egypt's ruling military council, the way forward was ambiguous, at best. And it was unclear just how much power he will have.
In recent days, Egypt's highest court ordered the new parliament, dominated by Islamists, to be dissolved. And the generals imposed constitutional changes that give themselves sweeping powers.