The EU's foreign policy chief Catherine Ashton headed to meet ousted Egyptian president Mohamed Morsi early Tuesday as his supporters rallied anew in Cairo.

A senior Egyptian source said the top diplomat was headed to visit the deposed leader, who has not been seen in public since his July 3 ouster.

In Cairo, meanwhile, Morsi's supporters marched towards security headquarters, despite warnings from authorities for them not to exceed their rights to peaceful protest.

Tensions have been running high since dozens were killed at a pro-Morsi rally in Cairo on Saturday.

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

The health ministry had earlier given a toll of 72.

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

In Cairo to discuss the political stand off, Ashton headed to meet Morsi in the early hours of Tuesday, a senior Egyptian official told AFP.

"She went to see him where he is being held. She isn't back yet," the source said on condition of anonymity, shortly after midnight.

Other sources told AFP that Ashton had left Cairo in a military helicopter heading to the undisclosed location where Morsi is being held.

The former president, deposed in a July 3 coup after massive protests against his rule, has not been seen publicly since his ouster.

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

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 demonstrators 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 had broken out, injuring 18.

The Anti-Coup Alliance of Islamist groups protesting against Morsi's ouster also called Monday for "a million person march under the banner of 'Martyrs of the Coup' on Tuesday."

They 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".

The call came after the National Defence Council warned 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".

The military also urged protesters not to "approach military facilities or units, (and) help us to protect your safety."

Ashton, who arrived in Cairo late Sunday, held talks with a string of officials throughout Monday, including interim president Adly Mansour, vice president for international affairs Mohamed ElBaradei and army chief General Abdel-Fattah al-Sisi.

On Monday night, she also met representatives of the pro-Morsi coalition, who said that "no initiatives" to resolve the crisis had been discussed.

The bloodshed in the Arab world's most populous nation has sparked mounting international concern.

"The United States strongly condemns the bloodshed and violence," the White House said in a statement, urging the interim government to respect demonstrators' rights.

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

"The interior minister should be dismissed and held accountable for his actions," the groups wrote. But they also urged Morsi supporters to "take action to persuade their colleagues and leaders to renounce" violence.

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 Monday, with the arrest of the president and vice president of the moderate Islamist Wasat party, which has protested the July 3 coup.

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

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.

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