Three people were killed in Cairo on Wednesday as clashes continue between security forces and protesters around Tahrir Square.

Despite promises of peace, riot police are trading volleys of tear gas with stones and makeshift firebombs from thousands of protesters gathered around the square.

On some sides of the square the protesters are respecting army barricades, as they demand an immediate end to the military's rule.

Egypt's military rulers have said they will replace police who have been firing on protesters, but so far there has been no sign of that change taking place.

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Ambulances continue to stream away from the square with those who have been injured in the fighting.

Clashes broke out in Mohammed Mahmud street, just off Tahrir Square, as riot police shot tear gas and birdshot, which ricocheted off concrete buildings, sending dust and chips of cement into tear gas-filled air, according to an AFP reporter.

Shadi al-Naggar, a doctor at the Omar Makram field hospital, said three people had died in the latest violence.

"It looked like live bullets, but I didn't get a chance to examine (them) before they were taken away to the hospitals," he said.

"One of them had his skull crushed."

A 10-year-old child was among the latest casualties, hit in the head by a live bullet, according to Father Fawzi Abdel Wahib at a church turned into a field hospital, although it was unclear if the boy had died.

"He was taken to the Qasr al-Aini hospital. He probably won't make it alive to the hospital," said Abdel Wahib.

The health ministry said in a statement issued Wednesday that a total of 32 people had died since the clashes began on Saturday. It gave a toll on Wednesday of two dead.

UN demands probe

The UN human rights chief Navi Pillay called on Wednesday for an independent probe into the killing of demonstrators by Egypt's military and security forces.

Field Marshal Hussein Tantawi, who served as defence minister under Hosni Mubarak but took power when the ex-president was ousted in February, pledged in a rare televised address on Tuesday night to hold a presidential election by the end of June - six months earlier than scheduled.

Field Marshall Tantawi said he was also ready to transfer power immediately, via a referendum, "should the people wish it."

But many among the tens of thousands of Egyptians attending an anti-military rally in Tahrir Square during his address said they did not believe a word he said.

"We can't trust what he says. The ball has been in SCAF's court for months, and they didn't do anything," said Ibtisam al-Hamalawy, 50, referring to the ruling Supreme Council of the Armed Forces.

Heba Morayef, a researcher for Human Rights Watch in Cairo, described the latest bloody confrontations as "very worrying."

"(Tantawi's) speech shows that the military is not ceding anything, and at the same time the ongoing violence is strengthening the protesters resolve."

Egyptian doctors treat protesters suffering from tear gas at field hospital in Tahrir Square. ( AFP: Khaled Desouki )

Unquestionable influence

Observers on Wednesday said that, while people demonstrating in Tahrir Square might not represent the majority of the Egyptian population, their influence was unquestionable.

"The continued spilling of blood has an effect. We are seeing middle class youth being killed, and that moves big segments in the cities and provinces," said Nabil Abdel Fatah, analyst at Al-Ahram Centre for Political and Strategic Studies.

Since Mr Mubarak's ouster, protesters have grown increasingly angry at the military council which they accuse of being an extension of the old regime and of resorting to Mubarak-era tactics to stifle dissent.

The latest mass protests resulted in the resignation of the cabinet, on Monday, just a week before crucial legislative polls, the first since Mr Mubarak was toppled, which Field Marshall Tantawi said would be held on schedule.

The SCAF had invited the country's political forces for crisis talks amid spiralling unrest that threatened to derail the election.

Protests also erupted on Tuesday in the Mediterranean city of Alexandria, the canal city of Suez and the central city of Qena, the northern city of Port Said and Assiut and Aswan in the south, as well as in the Nile Delta province of Daqahliya and the Red Sea resort of Sharm el-Sheikh.

Egyptian analyst and blogger Issander El-Amrani said the new demonstrations pointed to a dangerous stalemate between the army and the protesters.

"The military faces the same problem Mubarak did. They can't crush Tahrir, for domestic reasons and for international reasons," he said, saying that doing so would cause a "bloodbath."

ABC/AFP