CAIRO President Barack Obama called on Egypt's government and opposition on Saturday to engage each other in constructive dialogue and prevent violence spilling out across the region.
Bloodshed on Friday killed at least three people, including an American student, and mass rallies are planned for Sunday aimed at unseating Islamist President Mohamed Mursi.
Tens of thousands from both sides rallied again on Saturday across Egypt, although there were fewer reports of violence.
Obama said he was "looking at the situation with concern".
Hundreds have been wounded and at least eight killed in street fighting for over a week as political deadlock deepens. On Friday, a bomb killed a protester at a rally by the Suez Canal. Washington is pulling non-essential staff out of Egypt.
"Every party has to denounce violence," Obama said at the other end of Africa, in Pretoria. "We'd like to see the opposition and President Mursi engage in a more constructive conversation about how they move their country forward because nobody is benefiting from the current stalemate."
He added that it was "challenging, given there is not a tradition of democracy in Egypt".
Mursi's critics have dismissed U.S. calls for restraint as a sign of Washington backing Mursi, just as it backed Hosni Mubarak before he was deposed by people power in early 2011.
They now aim to repeat that feat, hoping millions will march to demand new elections on Sunday - when Mursi completes a year in power. They accuse his Muslim Brotherhood of hijacking the revolution and using electoral majorities to monopolize power.
"Egypt is the largest country in the Arab world," Obama said. "The entire region is concerned that, if Egypt continues with this constant instability, that has adverse effects more broadly." U.S. missions would be protected, he said. Last year, a consulate in Libya was overrun and Americans killed.
The Egyptian army is on alert. Funded by Washington for decades since a peace deal with Israel, the army warned politicians it may step in if they lose control of the streets - an outcome some in the diffuse opposition may quietly welcome, but to which Mursi's Islamist allies might respond with force.
The president met the head of the military on Saturday, along with the interior minister, to check security plans.
Protest organizers said on Saturday a petition calling on Mursi to quit had 22 million signatures - over 40 percent of the electorate and 7 million more than they announced 10 days ago.
The figure could not be verified, but independent analysts say there is a real prospect of very large demonstrations. Organizers have called for rallies in Cairo in the afternoon.
A few thousand activists were camping out at rival centers in the capital on Saturday. There was no sign of trouble, though some 40 were injured in scuffles at Beni Suef, to the south.
In the Sinai peninsula, near borders with Israel and the Gaza Strip, a police general was gunned down. The region's violence is emblematic of poor security since the revolution.
Several offices of Mursi's Muslim Brotherhood were attacked on Friday, including in Alexandria where American Andrew Pochter, 21, was fatally stabbed as he filmed events and another man died. In Port Said on the Suez Canal, a home-made grenade killed a protester.
The U.S. embassy evacuated non-essential staff and warned citizens to avoid Egypt. An airport source said dozens of U.S. personnel and their families left Cairo for Germany on Saturday.
The U.S. ambassador has angered liberals by saying Mursi was legitimately elected and that protests may be counter-productive for an economy crippled by unrest that has cut tourism revenues.
In the capital, Islamist supporters were still camped outside a suburban mosque where they had gathered in the many thousands on Friday to vent anger and fear over a return of army-backed rule. Some speakers also urged reconciliation.
They had their own security men, carrying staves and wearing protective gear, frisking visitors. One activist, Abdelhakim Abdelfattah, 47, said he hoped to avoid violence but that many Islamists would take to the streets if Mursi was under pressure.
"They'll come down to defend his legitimacy, not with weapons, but with their bodies," Abdelfattah said. "What's the nature of this legitimacy? The ballot box."
On Tahrir Square, seat of the uprising of early 2011, flags and tents form a base camp from where protesters plan to march to Mursi's office. Amr Riad, 26, said: "We're peaceful. But if those who come at us are violent we'll defend ourselves."
Liberal opposition leaders dismissed an offer of cooperation from Mursi this week as too little too late. The Brotherhood, which says at least five of its supporters have been killed in days of street fighting, accuses liberals of allying with those loyal to Mubarak to mount a coup against the electoral process.
A coalition of Islamist groups supporting Mursi said the violence of the past days confirmed there was "a conspiracy to spread chaos in the country and reproduce the defunct regime".
The opposition says the Brotherhood are trying to hoard power, Islamize a diverse society and throttle dissent. They cite as evidence Mursi's broadsides against critical media and legal proceedings launched against journalists and satirists.
With long lines for fuel adding to economic woes, activists hope millions of the less politically engaged will protest out of disappointment that the uprising has not brought prosperity.
Senior opposition figure and Nobel laureate Mohamed ElBaradei said in a message on YouTube Mursi's government had failed, and urged Egyptians to take to the streets peacefully on Sunday to get the revolution back on track.
"All Egypt needs to go out tomorrow to say we want to return to the ballot box, and to build the foundation of the house we will all live in," he said.
The opposition, which has lost a series of elections, wants to reset the rules that emerged in a messy process of army and then Islamist rule since Mubarak fell. It wants Mursi to make way for an interim administration led by a senior judge.
Egypt's leading religious authority warned of the risk of "civil war". A senior figure at Cairo's Al-Azhar institute said Sunday should be a day of dialogue, a "catalyst" for leaders to understand their duty - and the "dangerous alternative".
The head of the Coptic Church also called for dialogue and peace. Millions of Christians worry about new Islamic laws.
(Additional reporting by Yasmine Saleh, Omar Fahmy, Tom Perry, Patrick Werr, Shaimaa Fayed and Alastair Macdonald in Cairo, Abdelrahman Youssef in Alexandria and Yusri Mohamed in Ismailia, Jeff Mason, Mark Felsenthal and Pascal Fletcher in Johannesburg; Writing by Alastair Macdonald; Editing by Alison Williams)