Egypt has been rocked by further clashes between supporters of the Muslim Brotherhood-led government of Mohamed Morsi and opposition activists.

Four people were reported to have been killed and more than 300 people injured in Cairo during the violence which centred on the district around the presidential palace. The interior ministry said at least 32 people had been arrested and three police vehicles destroyed.

In the city of Ismailia, east of Cairo, protesters set alight the headquarters of Morsi's Freedom and Justice party which is dominated by the Brotherhood.

Mohamed ElBaradei, a leading opposition advocate of reform, accused Morsi's supporters of a "vicious and deliberate" attack against peaceful demonstrators.

"We hold President Morsi and his government completely responsible for the violence that is happening in Egypt today," he said.

"A regime that is not able to protect its people and is siding with his own sect, [and] thugs is a regime that lost its legitimacy and is leading Egypt into violence and bloodshed."

As dawn broke on Thursday at least four tanks were deployed outside the presidential palace, the Reuters news agency said, citing witnesses, and three armoured troop carriers were in the street outside the palace.

The opposition National Salvation Front, which ElBaradei is part of, is demanding Morsi rescind decrees giving him near unrestricted powers and shelve a disputed draft constitution that his Muslim Brotherhood allies passed last week.

The opposition says dialogue on Egypt's future can only begin once the decree has been rescinded. The decrees grant Morsi judicial immunity in all decisions and extended this legal protection to the constitutional assembly and the upper house of parliament, the shura council. Morsi has always insisted that it is a temporary measure that will automatically rescind when a constitution is passed.

The clashes in Cairo began after the vice-president, Mahmoud Mekki, spoke to the press to say that there would be no backing down by Morsi. But in a conciliatory gesture he added that amendments to disputed articles in the draft constitution could be agreed with the opposition.

A written agreement could then be submitted to the next parliament, to be elected after a referendum on the constitution on 15 December, he said.

Shortly after, the president's supporters moved against the opposition activists camped outside the presidential palace and the clashes, which lasted late into the night began. Witnesses said the two sides threw petrol bombs and stones at each other.

Mina Nader, an anti-Morsi protester, said: "The Brotherhood must be dragged in the streets like dogs, there is no salvation without blood after what they have done. Morsi must fall." Other protesters were heard chanting: "The people want the fall of the regime." Morsi's supporters shouted back: "Defending Morsi is defending Islam."

Earlier in the day three members of Morsi's advisory team resigned over the crisis. Seif Abdel Fattah, Ayman al-Sayyad and Amr al-Leithy all tendered their resignations, bringing to six the number of presidential staff who have quit in the wake of a decree that has triggered countrywide violence.

The previously announced resignations included a Christian and a woman. They were part of a presidential staff assembled by Morsi in an effort to build an inclusive administration. State institutions, with the partial exception of the judiciary, have mostly fallen in behind Morsi.

The army, the muscle behind all previous Egyptian presidents in the republic's six-decade history, has gone back to barracks, having apparently lost its appetite to intervene in politics.

The US, worried about the stability of a state that has a peace deal with Israel and to which it gives $1.3bn in military aid each year, called for dialogue. The US secretary of state, Hillary Clinton said dialogue was urgently needed on the new constitution, which should "respect the rights of all citizens". Clinton and Morsi worked together last month to broker a truce between Israel and Hamas in the Gaza Strip.

William Hague, the foreign secretary, called for restraint on all sides. He said Egypt's authorities had to make progress on the transition in an "inclusive manner" and urged dialogue. "We call on the Egyptian authorities to make progress on transition in an inclusive manner, which allows for a constructive exchange of views.

"We urge all parties to resolve their differences through a process of dialogue which allows all voices to be heard.