Egypt's military rulers apologised on Thursday for the deaths of demonstrators at the hands of police as a truce brought calm back to the outskirts of Cairo's Tahrir Square, scene of days of deadly clashes.

"An agreement has been reached between security forces and protesters to halt confrontations between the two sides," the cabinet said in a statement on Facebook.

At least 38 protesters have been killed since Saturday - when clashes erupted - and more than 2,000 injured, prompting expressions of concern from Western governments and a UN call for an independent inquiry into the 'excessive use of force'.

"The Supreme Council of the Armed Forces presents its regrets and deep apologies for the deaths of martyrs from among Egypt's loyal sons during the recent events in Tahrir Square," it said in a statement on its Facebook page.

"The council also offers its condolences to the families of the martyrs across Egypt."

Demonstrators again camped out overnight in Tahrir Square to demand the military leadership step down immediately.

Troops set up barricades during the night on Mohammed Mahmud Street, a flashpoint thoroughfare linking Tahrir with the heavily fortified interior ministry.

An army general pleaded with protesters to head back to the square - the symbolic heart of the uprising that toppled veteran president Hosni Mubarak in February.

"There are two fronts now: Mohammed Mahmud and Tahrir. We need to resolve what is happening in Mohammed Mahmud and go back to the square so we can focus on our goal of toppling the field marshal," said protester Sameh Mahmud, a 35-year-old lawyer.

At the entrance to Tahrir, protesters had set up their own barricades, applauding those returning from Mohammed Mahmud.

Since Friday, Egyptians have converged on the square to demand the end of military rule and the ouster of Field Marshal Hussein Tantawi, Mubarak's long time defence minister now in charge of the country.

The mass protests, which placatory moves by the military have failed to dampen, threaten to eclipse the first post-Mubarak parliamentary elections due to begin on Monday.

The army's apology came after a speech by Tantawi on Tuesday which was aimed at appeasing protesters in the square but was heavily criticised for not making mention of the deaths at the hands of police.

The SCAF vowed to investigate and prosecute all those behind the deaths.

It also pledged to offer assistance to the families of the dead and injured, and to set up a military field hospital in Tahrir.

The protest deaths prompted an unusually strongly worded statement from Al-Azhar, Sunni Islam's highest seat of learning, calling on police not to shoot at demonstrators.

Grand imam Sheikh Ahmed al-Tayyeb said that any dialogue 'stained with blood is doomed and its fruit will be bitter'.

Al-Azhar 'calls on the police leadership to immediately issue orders not to point their weapons at demonstrators... no matter what the reasons', Tayyeb said in a message aired on state television.

It calls 'on the armed forces to throw all their weight behind preventing confrontations between one people', he added.

Three people died in clashes with police in and around Tahrir on Wednesday, a medic said.

A fourth was shot dead in the northwestern city of Mersa Matruh when security forces clashed with demonstrators trying to storm a police station, state media said.

Clashes were also reported in the Mediterranean city of Alexandria, where hundreds of people protested outside the military headquarters, calling for the immediate transfer of power to a civilian administration.

UN High Commissioner for Human Rights Navi Pillay called the images coming out of Egypt 'deeply shocking', and urged the authorities to end their "clearly excessive use of force" against protesters.

British Foreign Secretary William Hague expressed deep concern at the 'unacceptable violence and loss of life' in and around Tahrir.

Egypt's military ruler had pledged in a rare televised address on Tuesday night to hold a presidential election by the end of June - six months earlier than scheduled.

Tantawi said he was also ready to transfer power immediately, through a referendum, 'should the people wish it'.

But thousands of protesters in Tahrir have continued to rail against him.

Analysts said that while the demonstrators in Tahrir might not represent the majority of the Egyptian population, their influence was unquestionable.

"We are seeing middle class youth being killed, and that moves big segments in the cities and provinces," said Nabil Abdel Fatah of the Al-Ahram Centre for Political and Strategic Studies.