Egypt's Muslim Brotherhood Thursday slammed the European Union's failure to denounce the military coup that ousted president Mohamed Morsi, after the bloc's foreign policy chief met Islamist officials and called for his release.

Catherine Ashton met senior pro-Morsi figures during her visit to Cairo on Wednesday, including former premier Hisham Qandil and representatives from the Freedom and Justice Party, the Brotherhood's political wing.

"The (FJP) delegation has expressed its surprise and condemnation of the official position of the European Union, which did not ... condemn the military coup that denied the Egyptian people their right to choose their president, their parliament, and their constitution," the party said.

Morsi's overthrow has deeply divided Egypt, between those who back the army's decision to topple the country's first democratically elected president on July 3 after massive nationwide protests, and his supporters who say the move was an affront to democracy.

Ashton also met Egypt's new leaders and members of Tamarod, the grass-roots movement behind the mass protests that led to Morsi's overthrow, and said the EU wanted Egypt to move "swiftly" towards an inclusive democratic process that engaged all factions.

Her visit came a day after Egypt's new 34-member cabinet was sworn in by interim President Adly Mansour.

Both the Muslim Brotherhood and the main Salafist party Al-Nur spurned calls to join the new administration, which the Brotherhood has rejected as illegitimate.

Ashton regretted that she was not able to meet Morsi, who has been held in custody since the military toppled him, and added her voice to those calling for his release, including the United States and Germany.

Washington has also pointedly refrained from saying Morsi was the victim of a coup, which would legally require a freeze on some $1.5 billion in US military and economic assistance to Cairo.

Speaking in Amman on Wednesday, US Secretary of State John Kerry said the Islamist president's removal had arisen out of an "extremely complex and difficult situation."

In the run-up to the coup, millions took to the streets accusing Morsi of concentrating power in the hands of the Muslim Brotherhood during his year in office, of sending the economy into free fall and of failing to protect minorities.

The political upheaval has enflamed tensions in the Arab world's most populous nation, with near daily protests by Morsi loyalists in the capital, where thousands of Islamists remained camped out at the Rabaa al-Adawiya mosque in Cairo's Nasr City.

More demonstrations are expected on Friday after the weekly main Muslim prayers.

Egypt has been rocked by violence since the coup, with 53 people killed last week, most of them Morsi supporters, when clashes erupted between Islamist protesters and the security forces outside a military barracks in Cairo.

The restive Sinai peninsula has been hit by a surge of deadly attacks, with militants killing three policeman in separate attacks on Wednesday night in the northern towns of El-Arish and Sheikh Zuweid.

Analysts attribute the Sinai violence, in which several security personnel, two Egyptian Christians and three factory workers have also been killed, to Islamist extremists seeking to take advantage of the political insecurity in Egypt.