Those killed included Helmi Masri Mohareb, a leader who transported militants across Egypt's southern border to join training camps, the interior ministry said in a statement.
The statement did not say when or exactly where in the desert they were killed, nor in which country they were alleged to have received training.
The security forces came under heavy fire as they pursued the militants, before shooting back at them, the ministry said.
The statement did not say whether there were any casualties among the security forces.
Mohareb is also wanted in several cases, and has received the death penalty pending the approval of the mufti, Egypt's official interpreter of Islamic law, though his opinion is not legally binding.
According to the statement, these groups were formed according to "assignments issued by the (Muslim Brotherhood) organisation's leadership abroad to its leadership in the country."
Then they were to "return to target state institutions, and government and Christian buildings, and a number of public figures and policemen, with the aim to create a state of chaos, instability, and to foment internal strife."
The Brotherhood, once Egypt's largest opposition movement, has long denied involvement in violence.
The Brotherhood's Mohamed Morsi was elected as Egypt's first civilian president in 2012, but the army overthrew him a year later following mass protests against the divisive Islamist's rule.
Analysts say a section of the Brotherhood has encouraged armed attacks against policemen in Egypt.
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