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The killings come a day after President Abdel Fattah al-Sisi blamed protests against his rule on "political Islam". State media has also accused the Muslim Brotherhood of stoking dissent.

In a brief statement, the ministry said police had exchanged fire with the "terrorist" group in October 6 City, on the southwestern edge of the capital, accusing it of "planning a series of terror operations".

After leading the 2013 coup that overthrew Egypt's first democratically elected president, Brotherhood member Mohammad Morsi, Sisi launched a widespread crackdown on the group.

More than a thousand of Morsi's supporters was killed in the Rabaa massacre in 2013 and thousands more members of the group have been detained and jailed after the Brotherhood was banned and deemed a terror organisation.

The Egyptian authorities regularly raid and kill suspects they say are armed affiliates of the group.

But Sisi's regime has been accused of extrajudicially killing hundreds of people in such "shootouts".

A report by Reuters in April indicated that several Egyptians accused of being armed members of the Brotherhood or extremist Islamist organisations such as the Islamic State group were civilians who "disappeared" weeks or months before they were killed in "shootouts" with the authorities.

Such accounts throw significant doubt on government reports of the killings of Muslim Brotherhood or IS members.

On the sidelines of the United Nations General Assembly in New York on Monday, Sisi was asked about the ongoing protests in his country.

"Let me say that you will always find something like this in our region, especially with political Islam," he said.

"I want you to rest assured that, especially in Egypt, the public opinion and the people themselves are refusing this kind of political Islam to Egypt. They have demonstrated their refusal before, and they refuse those to have control on the country for only one year."

Protests sweep Egypt

Unprecedented demonstrations calling for the ousting of Sisi erupted last week in Cairo, Suez and other Egyptian cities.

The protests were sparked by corruption allegations lodged against Sisi, his wife and the military by a former government contracter, now self-exiled in Spain.

Mohamed Ali has accused Sisi and his military of appropriating millions of dollars in public funds to build a colossal presidential palace and a number of luxurious villas.

More than 650 people have been detained since Friday in what has been dubbed the "Palacegate" revolution.