"It is not possible for us to talk now, while blood is being shed just meters away," said Essam el-Erian, a senior figure in the Brotherhood's political party.
Nevertheless, the ruling military council met with the other political factions to discuss efforts to create a new constitutional panel.
The violence also led to the cancellation of the first presidential debate, between Moussa and Abolfotoh, which had been scheduled for nationwide broadcast Thursday night.
In many ways, Wednesday's clashes were a repeat of previous violence over the 14 months since Mubarak's ouster — a peaceful, anti-military demonstration set upon by armed men as police or army troops looked on without intervening.
On Wednesday, the army and police did not move for hours to separate the two sides.
Of the 11 killed, nine died of gunshots to the head and two suffered stabbing wounds, according to medical officials and police reports. The gunshots to the head suggested sniper fire.
Theories of who is behind the attacks of the past year have varied, with many activists blaming plainclothes police, army troops or petty criminals working for the police. Others spoke of hard-core Mubarak loyalists or thugs hired by Mubarak-era businessmen who have been hurt by the overthrow of the regime.
Abbasiyah residents and the protesters traded accusations of tit-for-tat attacks and intimidation.
"Salafis attacked us and our houses. They sealed off our streets, checking our IDs and damaging our shops and pharmacies. We were afraid. I am forced to arm myself," said one resident, driver Essam Bakheit. "They say we are thugs but I swear we are not. I was born here. They are liars."
Mohammed Fathi, a bearded Abu Ismail supporter, said the protesters did not instigate the violence. "Every night since we held our first day of protest, thugs climb the bridge above us and shower us with bombs and gunshots," he said.
The clashes broke out at dawn when assailants set upon several hundred protesters, security officials and witnesses said. The clashes resumed later in the morning, but then stopped again when lines of black-clad riot police and army troops backed by armored vehicles finally moved in to separate the two sides at noon.
"The army's intervention has come hours too late," Amnesty International spokesman Philip Luther said in a statement. "There appears to be no will within Egypt's ruling Supreme Council of the Armed Forces to prevent these tragic events."
Sami Mahmoud, a 42-year-old Abbasiyah resident, said he was standing guard outside his building early Wednesday when a group of armed men roamed the streets shooting in the air and at balconies.
"Nobody protected us. The military and police didn't intervene. They let us down," he said.
AP correspondents Maggie Michael and Sarah El Deeb contributed to this report.