Political violence on Friday killed three people, including an American student, and mass rallies are planned for Sunday aimed at unseating Islamist President Mohamed Mursi.
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 hope millions will march on Sunday when he marks a year in power to demand new elections. They accuse his Muslim Brotherhood of hijacking the revolution of 2011 and using its electoral majorities to monopolise 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, heavily funded by Washington since before Hosni Mubarak was overthrown, is on alert. It warned politicians it may step in if they lose control of the streets - an outcome some in the diffuse opposition coalition may quietly welcome, but to which Mursi's Islamist allies might respond with force.
It is unclear how big the rallies will be or when they may start. Protest organisers 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.
Some few thousand activists in Cairo were camping out at rival centres on Saturday. There was no sign of renewed trouble.
Several offices of Mursi's Muslim Brotherhood were attacked on Friday, including one in Alexandria where two men died, including 21-year-old American Andrew Procter. In Port Said on the Suez Canal, a home-made hand grenade killed a protester and wounded 15.
The Health Ministry said 236 people were injured on Friday.
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.
On Tahrir Square, seat of the uprising of early 2011, flags and tents formed a base camp for protesters. They hoped for millions on the streets under slogans accusing Mursi and the Brotherhood of hijacking the revolution against Hosni Mubarak to entrench their own rule. A rally was also planned outside the presidential palace, where some had already taken up position.
With short supplies of fuel adding to long-standing economic woes, many said they would turn out on Sunday, when Mursi marks his first year in office as Egypt's first ever freely elected leader, to demand a new president who can bring them prosperity.
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.
The opposition says the Brotherhood are trying to monopolise power, Islamise a diverse society and throttle dissent. They cite as evidence Mursi's broadsides against critical media and legal proceedings launched against journalists and satirists.
"Mursi is no longer the legitimate president of Egypt," Mohamed Abdelaziz, a protest organiser, told a news conference where others called for peaceful sit-ins to last until Mursi made way for an interim administration led by a senior judge.
"Come June 30, the people will run Egypt!" chanted people attending the event. 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 early 2011.
Egypt's leading religious authority warned of the risk of "civil war" after violence in the past week that left several dead and hundreds injured. The clerics backed Mursi's offer to talk to opposition groups before Sunday's protests.
A senior figure at Cairo's Al-Azhar institute said Sunday should be a day of "community dialogue and civilized expression of opinion", a "catalyst" for political leaders to understand their national duty - and the "dangerous alternative".
Senior Brotherhood figure Essam el-Erian was dismissive of middle-class protest organisers in a Facebook post: "Millions of farmers will wake early, perform their morning prayers and go to their fields to harvest food for the people," he wrote.
Warning again that Mubarak-era "thugs" would spread violence among peaceful protesters, he said government would continue: "President Mohamed Mursi will go to his office tomorrow to sign new planning and budget laws for the new financial year."
Medical and security officials in Alexandria, Egypt's second city, said the American was fatally stabbed as he filmed events at the Brotherhood office in the Mediterranean port during an attack by anti-Mursi protesters, who eventually ransacked it.
Kenyon College in Ohio said Pochter was one of its students and came from Chevy Chase, Maryland. A Facebook post apparently from his family said Pochter had been teaching English to 7- and 8-year-olds and had been improving his Arabic:
"As we understand it, he was witnessing the protest as a bystander and was stabbed by a protester."
Additional reporting by Yasmine Saleh, Alexander Dziadosz, Omar Fahmy, Tom Perry, Patrick Werr, Shaimaa Fayed and Alastair Macdonald in Cairo and Yusri Mohamed in Ismailia; Writing by Alastair Macdonald