The EU foreign policy chief held two hours of talks with the ousted Egyptian president as she pressed efforts on Tuesday to broker an end to an increasingly bloody crisis.

Catherine Ashton's intensive talks with leaders of both the army-installed interim government and the Islamist opposition came as supporters of Mohamed Morsi vowed no let-up in their demonstrations for his reinstatement despite weekend clashes that left 82 people dead.

Ashton's spokeswoman did not say where the EU envoy met Morsi, who has been in custody since just hours after his overthrow in a July 3 coup.

She met him "for two hours," spokeswoman Maja Kocijancic said, without elaborating on the content of the talks.

Sources told AFP that Ashton had left Cairo in a military helicopter late on Monday for the undisclosed location where Morsi is being held.

On her last visit on July 17, Ashton unsuccessfully requested to meet the ousted president and urged his release.

Morsi is being held on suspicion of crimes relating to his escape from prison during the 2011 uprising that overthrew president Hosni Mubarak.

His supporters have rallied daily for his reinstatement and on Monday marched from a key Cairo sit-in to several security headquarters.

The marches raised fears of fresh clashes, but protesters kept their distance from security forces and headed back to their protest tent city after the demonstrations.

In the eastern city of Ismailia, however, a security source said clashes between Morsi supporters and opponents broke out, injuring 18.

The Anti-Coup Alliance called for a million-man march later on Tuesday under the banner of "Martyrs of the Coup" to commemorate its dead at a rally in Cairo on Saturday.

It urged Egyptians "to go out into the streets and squares, to regain their freedom and dignity -- that are being usurped by the bloody coup -- and for the rights of the martyrs assassinated by its bullets".

Khaled al-Khateeb, the head of the central administration of Egypt's emergency services, revised Saturday's death toll up to 82, including a police officer who died of his wounds.

The White House "strongly" condemned the bloodshed, and urged the military-backed interim government to respect the rights of demonstrators.

The interim National Defence Council has urged protesters "not to exceed their rights to peaceful, responsible expression of their opinions," warning that they would face "decisive and firm decisions and actions in response to any violations".

Ashton, who arrived in Cairo late Sunday, held intensive meetings throughout Monday, including with army chief General Abdel Fattah al-Sisi and army-installed interim president Adly Mansour.

She also met representatives of the pro-Morsi coalition, which said that "no initiatives" to resolve the crisis had been discussed.

"The coalition affirmed the Egyptian people will not leave streets and squares until constitutional legitimacy returns," the Islamist bloc said in a statement on Tuesday.

The persistent standoff has sparked mounting international concern and growing domestic criticism of the interim authorities.

A group of Egyptian NGOs called on Monday for Interior Minister Mohamed Ibrahim to be sacked for what it called Saturday's "massacre".

In its first comments on the bloodshed, the interim presidency said Sunday that it was "saddened" by the deaths, but dubbed the protest area where they occurred a "terror-originating spot".

A crackdown on Morsi supporters continued on Monday, with the arrest of the president and vice president of the moderate Islamist Wasat party, which has protested the July 3 coup.

In the Sinai Peninsula meanwhile, a security source said two policemen were killed in separate shooting attacks in El-Arish.

And in Cairo, 15 people were killed in a brawl between street vendors and shop owners over space -- including 13 who died in a fire.