The Muslim Brotherhood announced the decision in a statement on Wednesday, after presidential spokesman Ahmed al-Muslimani said that Beblawi had announced that some cabinet posts would be offered to the Muslim Brotherhood.
“We reject all that comes from this coup,” spokesman for the Muslim Brotherhood, Tareq al-Morsi, said in response.
The group said that it will not hold talks with the interim government until ousted President Mohamed Morsi is reinstated.
Also on Wednesday, Egypt’s main liberal coalition, the National Salvation Front (NSF), retracted an earlier statement that rejected a constitutional decree issued by the interim government.
The decree, issued by interim President Adli Mansour, lays out a timetable for the transition, the period of which is to last around six months until a presidential election is held.
Meanwhile, the interim prime minister said the new cabinet is unlikely to have unanimous support.
On July 3, Egyptian army chief General Abdel Fattah al-Sisi announced that Morsi was no longer in office and declared that the head of the Supreme Constitutional Court, Adli Mahmoud Mansour, had been appointed as the new interim president of Egypt.
On July 9, interim President Mansour appointed 76-year-old former Finance Minister Beblawi as the country’s interim prime minister and 71-year-old opposition politician Mohamed ElBaradei as deputy to the president.
Since last week, Egypt has been the scene of rival rallies and clashes between thousands of the supporters and opponents of ousted Morsi.
Egyptian officials say that on July 8, 84 people were killed in clashes between the supporters of Morsi and security forces in Cairo.
Morsi is reportedly being held “preventively” by the military. Senior army officials say he might face formal charges over accusations made by his opponents.