The European Union's foreign policy chief was in Cairo on Monday, the first senior overseas envoy to visit Egypt's new rulers since the weekend killing of at least 80 supporters of the country's deposed Islamist president.

The killings at dawn on Saturday have triggered global anxiety that the Arab world's most populous country faces wider conflagration after the military overthrew Mohammed Morsi on July 3.

Catherine Ashton, the EU's chief diplomat, was scheduled to meet with General Abdel Fattah al-Sisi, the head of the Egyptian armed forces who ousted Morsi, interim president Adli Mansour and officials of the Freedom and Justice Party, the Muslim Brotherhood's political wing.

Ashton said in a statement she would press for a "fully inclusive transition process, taking in all political groups, including the Muslim Brotherhood".

It was unclear what leverage Ashton has. The United States is Egypt's chief Western backer and source of military aid, but the EU is the biggest civilian aid donor to Egypt.

The EU has attempted to mediate in Egypt's political crisis over the past six months as Egyptians have grown increasingly suspicious of US involvement.

Underscoring the risk of more bloodshed, several thousand supporters of Morsi's Muslim Brotherhood threatened to march on the military's intelligence headquarters in defiance of a warning from the army to stay away.

They turned back early on Monday, having left the site of a Brotherhood vigil in northern Cairo chanting, "Our blood and souls we sacrifice for Morsi".

The Anti-Coup Alliance of Islamist groups urged demonstrators to march on security buildings on Monday night and called a million-man march for Tuesday.

Their statement came after the National Defense Council warned on Sunday that it would take "decisive and firm action" against demonstrators if they went beyond their right to peaceful protest.

The Health Ministry said on Monday that 80 people were killed in the early hours of Saturday, up from a previous toll of 72, when security forces opened fire on marchers.

Egypt's army-installed authorities have vowed to clear them from the site after complaints from residents about the huge encampment on their doorstep.