The Brotherhood is planning three consecutive Fridays of large scale protests in Cairo to build pressure on the military.
"We will continue our peaceful resistance to the bloody military coup against constitutional legitimacy,'' said a statement issued on its official website on Thursday.
''We trust that the peaceful and popular will of the people shall triumph over force and oppression.''
The BBC reports supporters demanding Mr Morsi's reinstatement have been staging mass protests in Cairo near a barracks where he is believed to be held. Fifty one were killed there after dawn prayers on Monday.
A timetable for new elections was announced in a constitutional declaration by interim President Adly Mansour on Monday evening. It laid out plans to set up a panel to amend the suspended constitution within 15 days.
The changes would then be put to a referendum - to be organised within four months - which would pave the way for parliamentary elections, possibly in early 2014.
Once the new parliament convenes, elections will be called to appoint a new president.
The BBC reports the Brotherhood has rejected the transition plan and its Freedom and Justice Party has said it will turn down a post in the cabinet being formed by interim Prime Minister Hazem al-Beblawi.
US comment
Meanwhile, the US State Department said on Thursday that politically motivated arrests in Egypt this week make it difficult to see how the country will be able to move beyond the current political crisis.
It says the trageting of specific groups for arrest is not in line with the national reconciliation that the interim government and the military say they are pursuing.
Mr Morsi was deposed by the army last Wednesday, a few days after the first anniversary of his election in 2010.
