The US and EU are trying to mediate a peaceful resolution to the standoff to avoid a repeat of deadly clashes between Morsi's supporters and security forces that have killed at least 250 people since the army shunted Morsi aside.
But Egypt's National Defence Council said the search for a peaceful resolution is not open-ended, and that a negotiated end would not shield what it called "law-breakers'' and others who incite against the state from legal proceedings.
Sunday's statement by the National Defence Council is the latest warning to the pro-Morsi protesters. The statement suggested that the window for a negotiated end to the pro-Morsi sit-ins on opposite sides of the Egyptian capital was narrowing and not open-ended.
It said a chance should be given to all "negotiations and mediations'' that could end the protests without bloodshed. But it said the timeframe should be "defined and limited and ... not infringe on the law and the rights of citizens.''
The statement called on protesters to abandon the sit-ins and join the political road map.
Nobel winner denied entry
Egyptian authorities denied Yemen's Nobel Peace Prize winner Tawakkul Karman entry into Egypt after she landed at Cairo airport on Sunday, airport officials said.
Karman, the first Arab woman to win the Nobel Peace prize, has stated her opposition to the military's ouster of Morsi and said she had intended to join the larger of two sit-in protests by Morsi's supporters in Cairo. The airport officials said she was sent back on the Sunday flight that brought her to Cairo from the UAE. They gave no reason for denying her the entry, saying only that her name had been placed on the stop list. AP