CAIRO — The Muslim Brotherhood’s powerful political wing has backed down from demands that Egypt’s new parliament should have the right to quickly replace the military-appointed government.

The secretary general of the Freedom and Justice Party, which is poised to win by far the most seats of any party in the lower house of the next parliament, said that the party wants to avoid conflict when the legislature is seated Jan. 23 and get through the transitional phase without angering the country’s military rulers.