The United States has criticised the recent violence in Egypt, where 72 people were killed in an attack on a rally in favour of ousted president Mohamed Morsi.
"The United States strongly condemns the bloodshed and violence" in Cairo and Alexandria, the White House said in a statement on Monday, urging the military-backed interim government to respect the rights of demonstrators.
Egypt's health ministry put the death toll at 81 across the country, with 72 deaths in Cairo and nine in Alexandria.
The Muslim Brotherhood have put the death toll much higher, saying at least 120 people were killed.
Egypt has been violently polarised since the July 3 overthrow of Morsi, the country's first democratically elected president, in a military coup triggered by massive demonstrations against his year-long rule.
Cairo and the northern city of Alexandria have since seen massive rival rallies that have often turned violent, with Morsi supporters battling political opponents and the police.
The United States has refrained from calling Morsi's overthrow a "coup", which would require the freezing of some $1.3 bn in annual military aid, instead calling for a swift transition to elected, civilian rule.
Morsi hails from the Muslim Brotherhood, one of the region's largest and best organised Islamist movements, which prevailed in a series of elections held after the secular autocrat Hosni Mubarak was toppled in a popular uprising in 2011.
Supporters of Morsi, who has been held incommunicado since his overthrow, have called for a million-man march on Tuesday, raising fears of more street clashes, and after authorities warned of "decisive" action if protesters are considered a threat.
In a statement, the Anti-Coup Alliance of Islamist groups 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 Anti-Coup Alliance also called for protesters to march to security buildings in provinces across Egypt on Monday night "to condemn the criminal acts and the firing of live ammunition by the interior ministry at peaceful demonstrators".
The military issued its own warning to Cairo protesters in flyers dropped from helicopters early on Monday.
"We call on you not to approach military facilities or units, help us to protect your safety," it said, addressing protesters as "honourable sons of the nation".
A group of Egyptian NGOs issued a statement on Monday calling for interior minister Mohamed Ibrahim to be dismissed over what it called a "massacre," but also urged the Brotherhood to denounce violence.
"The interior minister should be dismissed and held accountable for his actions," the groups wrote, urging 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 on 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 two leaders of the moderate Islamist Wasat party, president Abul Ala Mady and vice president Essam Sultan.
State news agency MENA said they were being investigated on suspicion of inciting violence and murder.
With tensions rising, EU foreign policy chief Catherine Ashton held discussions with a range of government and opposition figures.
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She met interim president Adly Mansour, as well as members of the Tamarod group that organised protests calling for his removal, and the April 6 movement.
Beshir Abdel Fattah, editor in chief of Democracy Review magazine, told Al Jazeera from Cairo, "The EU has more credibility than the US right now, especially as the US refuses to label what happened on 3rd July as a coup."
"Therefore, I think the EU can say something that will be listened to by both sides."
In a statement, Ashton said she would be calling for "a fully inclusive transition... including the Muslim Brotherhood".
She added that this process must lead as fast as possible to a constitutional system and free and fair elections and a civilian government
"I will also repeat my call to end all violence. I deeply deplore the loss of life," she said.
The Brotherhood's political arm, the Freedom and Justice Party, confirmed it would meet with Ashton on Monday on the basis of "constitutional legitimacy and in pursuit of an end to the military coup".
The group has insisted that it will not accept any solution to the crisis that does not involve Morsi's return to office.