Police and protesters demanding that Egypt's ruling military council step down are observing a truce after five days of deadly street battles in which at least 40 people died.

Egypt's military also issued a statement today apologising for the loss of life and vowing to bring to justice those responsible for the deaths of protesters in Cairo's iconic Tahrir Square and elsewhere in the country.

Army troops have used metal bars and barbed wire to build barricades to separate protesters and police on side streets leading from Tahrir to the nearby interior ministry. Most of the fighting has been taking place on those side streets.

The truce came into force around 6am and was still holding by late morning.

The truce came into effect after international criticism of Egypt's military rulers mounted, and a rights group raised the death toll for the wave of violence to at least 38.

The United Nations strongly condemned what it called an excessive use of force. Germany, one of Egypt's top trading partners, called for a quick transfer of power to a civilian government. The United States and the UN secretary general expressed their concern over the use of violence against mostly peaceful protesters.

Navi Pillay, the UN High Commissioner for Human Rights, deplored the role of Egypt's security forces in attempting to suppress protesters.

"Some of the images coming out of Tahrir, including the brutal beating of already subdued protesters, are deeply shocking, as are the reports of unarmed protesters being shot in the head," she said.

"There should be a prompt, impartial and independent investigation, and accountability for those found responsible for the abuses that have taken place should be ensured."

She said the actions of the military and police were enflaming the situation, prompting more people to join the protests.

"The more they see fellow protesters being carted away in ambulances, the more determined and energised they become."

Clashes had resumed yesterday despite a promise by the head of the ruling military council to speed up a presidential election to the first half of next year, a concession swiftly rejected by tens of thousands of protesters in Tahrir Square.

The military previously floated late next year or early 2013 as the likely date for the vote, the last step in the process of transferring power to a civilian government.

The clashes are the longest spate of uninterrupted violence since the 18-day uprising that toppled the former regime in February.

The stand-off at Tahrir and in other major cities such as Alexandria and Assiut has deepened the country's economic and security crisis less than a week before the first parliamentary elections since the removal of former leader Hosni Mubarak.

Field Marshal Hussein Tantawi tried to defuse tensions with his address late on Tuesday, but he did not set a date for handing authority to a civilian government.

The Tahrir crowd, along with protesters in a string of other cities, want Tantawi to step down immediately in favour of an interim civilian administration to run the nation's affairs until a new parliament and president are elected.

The government offered more concessions, ordering the release of 312 protesters detained over the past days and instructing civilian prosecutors to take over a probe the military started into the death of 27 people, mostly Christians, in a protest on October 9. The army is accused of involvement in the killings.

The military also denied that its troops around Tahrir Square used tear gas or fired at protesters, an assertion that runs against numerous witness accounts that say troops deployed outside the interior ministry were firing tear gas at protesters.