Supporters demanding Morsi's reinstatement have been staging mass protests in Cairo near a barracks where he is believed to be held.
The Muslim Brotherhood statement comes a day after warrants were issued for the arrest of other senior figures.
On Monday, more than 50 Morsi loyalists were killed in clashes with the army.
Morsi's removal - a year after he was elected - followed protests by millions of people across Egypt.
In other developments, US officials said Washington would press on with plans to deliver four F-16 fighter jets to Egypt in the next few weeks despite the political unrest in the country.
The Obama administration is continuing to evaluate the events which happened in Egypt last week.
Massive US military aid to Cairo would legally have to be cut if the removal of the Islamist leader is determined by Washington to have been a coup.
"We will continue our peaceful resistance to the bloody military coup against constitutional legitimacy,'' said a statement issued on the Muslim Brotherhood's official website on Thursday.
"We trust that the peaceful and popular will of the people shall triumph over force and oppression.''
The new authorities have not specified where Morsi is, but a foreign ministry spokesman said he was in a "safe place" and being treated in a "very dignified manner".
On Wednesday, arrest warrants were issued for the Muslim Brotherhood's spiritual leader, Mohammed Badie, and nine other senior figures.
They are charged with inciting Monday's deadly violence in the capital, in which more than 50 Brotherhood supporters, a soldier and two policemen died.
The Brotherhood says the army fired on peaceful demonstrators and it is accusing the interim authorities of a cover up.
The military, however, says soldiers acted in self-defence after being attacked by armed assailants.
Many Brotherhood members are already in detention and warrants are said to have been issued for hundreds more.
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