The lawyer, Mohammed Zyan, told dpa that the detainees wanted to take a stand against the Moroccan authorities.
However, it is not legal for anyone to request that they be stripped of citizenship, he added.
On Saturday, the father of Nasser Zefzafi, the leader of the protest movement, known as Hirak Rif, posted a video on his Facebook page in which he appeared reading out a message from the six detainees.
In the message, the detainees said that they would relinquish their citizenship, go on a hunger strike and renege on their allegiance to the Moroccan king.
They held the authorities responsible for their safety and called on the international community for support.
Last month, Morocco’s King Mohammed VI pardoned thousands of detainees, including some arrested over 2016 anti-government protests, in a move to mark his 20 years on the throne.
In 2016, a wave of street protests erupted in the northern province of al-Hoceima against unemployment and alleged government corruption.
The protests followed the death of a fish vendor who was crushed by a waste disposal truck while trying to prevent the destruction of his fish, which were confiscated by police.
The protests were some of the largest seen in Morocco since 2011.
(Edited by Emmanuel Yashim)