The office of President Mohamed Morsi said Sunday dialogue is the only way out of Egypt's political crisis, while the opposition urged protesters to stay on the streets as hundreds of thousands rallied to demand the Islamist leader's ouster.

"Dialogue is the only way through which we can reach an understanding... The presidency is open to a real and serious national dialogue," presidential spokesman Ehab Fahmy told reporters.

Ethiopia is hoping that talks with Egypt will ease a row over sharing the waters of the Nile, Foreign Minister Tedros Adhanom said on Sunday during a trip to Algeria.

But Tedros did not rule out "international mediation" if the talks founder.

Thousands of demonstrators waved red cards in Tahrir Square Sunday to demand the resignation of Egypt's Islamist President Mohamed Morsi, as the spirit of 2011's revolution returned to the iconic Cairo protest venue.

"The people want the ouster of the regime!" protesters chanted -- the signature slogan of the uprising that ousted Hosni Mubarak and brought Morsi to power.

Mohamed Morsi, an Islamist who pledged to be a "president for all Egyptians" at his inauguration, faces mass rallies demanding his departure on Sunday's first anniversary of his taking office.

Twelve months after he was feted by cheering crowds in Cairo's iconic Tahrir Square, Morsi's Egypt is deeply divided and rocked by deadly violence that has killed eight people this week alone.

Egyptians flooded the streets on Sunday determined to oust Islamist President Mohamed Morsi on the anniversary of his turbulent first year in power, in the biggest protests Egypt has seen since the 2011 revolt.

A sea of jubilant protesters converged on Cairo's Tahrir Square and the large avenue outside the presidential palace, as well as in several others squares of the capital as army helicopters circled overhead.

Gunmen shot and killed an Egyptian police officer during an ambush Saturday in the Sinai peninsula, a security source said, the second attack on police in the restive region this month.

"Colonel Mohammed Hani, a high-ranking officer, was killed by six bullets to the head when unknown gunmen opened fire on him with machine guns," the source said.

More than 22 million people have signed a petition in Egypt demanding the departure of Islamist President Mohammed Morsi and a snap election, the opposition Tamarod (Arabic for rebellion) group said on Saturday.

"Our petition has gathered 22,134,465 signatures," Tamarod spokesman Mahmoud Badr told journalists on the eve of Sunday's first anniversary of Morsi's inauguration when it has called for nationwide protests.

U.S. President Barack Obama Saturday expressed concern about clashes in Egypt and called on President Mohamed Morsi to be more "constructive" along with the opposition to end the political crisis.

"We are all looking at the situation there with concern," Obama said in South Africa, adding that the U.S. government had taken steps to ensure the safety of its embassy, consulates and diplomats in Egypt.

Washington warned against travel to Egypt after an American was among three people killed during rival demonstrations for and against Islamist President Mohamed Morsi ahead of Sunday's anniversary of his turbulent maiden year in office.

The U.S. State Department also authorized the departure of non-essential embassy staff for fear of further deadly violence in the face of the bitter antagonism between Morsi's Islamist supporters and the mainly secular opposition.

Egyptian Islamist parties are set to begin an open-ended demonstration on Friday in support of President Mohammed Morsi, two days before planned rallies against him, highlighting the country's deep divisions.

An alliance of Islamist parties and groups called the rallies outside the Rabaa al-Adawiya mosque in Cairo's Nasr City district under the slogan "legitimacy is a red line".