Egypt's ultraconservative Al-Gamaa Al-Islamiya and its political arm the Building and Development Party have called upon interim president Adly Mansour to step down to spare Egypt a "bitter conflict."
The group said in an official statement on Sunday that it did not expect that Mansour, who headed the High Constitutional Court before taking the presidential oath on Thursday, would accept the presidency.
The Egyptian Armed Forces deposed President Mohamed Morsi on Wednesday following nationwide protests calling for his ouster.
Al-Gamaa Al-Islamiya, which is part of the recently-formed National Alliance to Support Legitimacy, a coalition spearheaded by the Muslim Brotherhood in support of Morsi, said that Mansour's resignation would help lead the country out of "the current crisis and prevent chaos."
Since Morsi's removal, street battles between rival factions have killed at least 37 people and injured over 1,400.
On Sunday, mass rallies led by both supporters and opponents of Morsi are expected to take place nationwide.