The European Union foreign policy chief has urged Egypt's military-backed interim government and the Muslim Brotherhood to take part in an “inclusive political process” to settle the turmoil in the country.

“It is important to find ways to have the right kind of dialogue and that's what we have been urging everyone,” Catherine Ashton told reporters after meeting with Egypt's Armed Forces Chief General Abdel-Fattah al-Sisi in the Egyptian capital Cairo on Thursday.

“My guess is that process will take a little time to do but it's important for everybody to feel that they are able to participate in the process as well as ultimately in political life,” added Ashton.

Ashton, who and several other Western envoys failed in August to convince the military to avoid using force against supporters of former president, Mohamed Morsi, said the European Union was not involved in mediating any talks.

Ashton wrapped up a two-day visit to Egypt, her third visit to the North African country since last three months, after holding talks with Egyptian top officials including interim President Adly Mansour and liberal and Islamist politicians.

Amr Darrag, a Muslim Brotherhood politician, who met Ashton on Wednesday, said there had been no talk of “initiatives or solutions”, saying, “We continue to say that Morsi is the elected president.”

Egypt has been experiencing unrelenting violence since July 3, when the army ousted Morsi, suspended the constitution, and dissolved the parliament. It also appointed the head of the Supreme Constitutional Court, Mansour, as the new interim president.

The government of Mansour has launched a bloody crackdown on Morsi supporters and arrested more than 2,000 Brotherhood members, including the party’s leader, Mohamed Badie, who was detained on August 20.

About 1,000 people were killed in a week of violence between Morsi supporters and security forces after police dispersed their protest camps in a deadly operation on August 14.

The massacre sparked international condemnation and prompted world bodies to call for an independent investigation into the violence.