Raising the prospect of more bloodshed, the Brotherhood said it would march again on Monday evening towards a military intelligence headquarters.
Catherine Ashton, the European Union's foreign policy chief, became the first overseas envoy to visit the Egypt since Saturday's carnage, the second mass killing of Mursi supporters by security forces since he was overthrown by the army on July 3.
The bloodshed has triggered global anxiety that the army may move to crush the Muslim Brotherhood, which emerged from decades in the shadows to win power in the wake of Egypt's 2011 Arab Spring uprising against Hosni Mubarak.
Ashton, on her second trip to Egypt since Mursi's fall, met General Abdel Fattah al-Sisi, the head of the army and the man behind the overthrow of Egypt's first freely elected president. She also held talks with deputy interim president and prominent liberal politician Mohamed ElBaradei and interim Foreign Minister Nabil Fahmy.
There were no immediate details on the talks. Earlier, Ashton said she would press for a "fully inclusive transition process, taking in all political groups, including the Muslim Brotherhood".
In comments carried by the MENA state news agency, ElBaradei said he had told Ashton that the country's new leadership was doing all in its power to "reach a peaceful way out of the current crisis, that preserves the blood of all Egyptians."
Ashton was also expected to meet members of the Freedom and Justice Party, the Muslim Brotherhood's political wing.
Her leverage is limited. The United States is Egypt's chief Western backer and source of $1.3 billion in military aid, though the EU is the biggest civilian aid donor to the country, the Arab world's most populous and a strategic bridge between the Middle East and North Africa.
The EU has attempted to mediate in Egypt's political crisis over the past six months as Egyptians have grown increasingly suspicious of U.S. involvement.
Mursi has been in detention since he was ousted and the military-backed interim government has placed him under investigation on charges that include murder.
The handling of him by the military suggests it believes it has the support of the majority of Egyptians. They turned out in huge numbers to protest against the Islamist leader before the army moved against him.
Army chief Sisi has emerged as the public face of the new order, enjoying fawning coverage in the Egyptian media and sowing doubts about the military's pledge to hand over to full civilian rule with a "road map" to parliamentary elections in about six months.
The Muslim Brotherhood says it wants nothing to do with the proposed transition, and thousands of its supporters have been camped out for a month at the Rabaa al-Adawiya mosque in northern Cairo demanding Mursi's reinstatement.
Dozens were shot dead by security forces at dawn on Saturday when they marched from the vigil after a day of rival mass rallies. The Health Ministry on Monday put the death toll at 80, up from 72. Nearly 300 people have died in violence since Sisi deposed Mursi.
Saturday's bloodshed was the worst since July 8, when security forces killed more than 50 Brotherhood supporters outside a Cairo barracks.
"The danger we face because of the political situation and the coup is greater than the violence we face in marches," said Brotherhood member Islam Tawfiq, 26.
Egypt's army-installed interim cabinet has vowed to clear the Brotherhood's mosque vigil after complaints from residents about the huge encampment on their doorstep.
Besides Mursi, other Brotherhood leaders are also being held, and in the early hours of Monday police arrested two senior members of the Islamist Wasat Party, allies of Mursi, the MENA news agency reported.
The round-up of Islamist leaders and Saturday's deaths have stirred fears that the military plans to drive the Muslim Brotherhood back underground, risking more instability in the country of 84 million people.