President Mohamed Morsi of Egypt has vowed to stay in power and defend his constitutional legitimacy.
In a late-night televised appeal for calm on Tuesday, Mohammed Morsi rejected an army ultimatum that the crisis be resolved by Wednesday.
Mr Morsi admitted he had made mistakes, but said he would not be dictated to and urged protests to remain peaceful.
The army earlier leaked details of a draft "roadmap" for Egypt's future.
Details of the plan leaked to the BBC outlined new presidential elections, the suspension of the new constitution and the dissolution of parliament.
Clashes in Cairo between opponents and supporters of the president resulted in at least seven deaths on Tuesday.
The army warned on Monday that it would step in unless a solution was found, giving Mr Morsi 48 hours to find agreement with the opposition.
That ultimatum expires around 4.30pm (15:30 BST) on Wednesday.
The BBC reports tens of thousands of protests on both sides have been back out on the streets.
In a 45-minute address on state television, Mr Morsi said he respected the right to peaceful protest, but said respect for the constitutional order was the "only guarantee against further bloodshed".
"When there's violence and thuggery I must act," he said.
He blamed the unrest on corruption and remnants of the ousted regime of Hosni Mubarak, and called for protesters to respect the rule of law.
The BBC reports the army has cited the need to avoid bloodshed as its main motivation. It is also worried by other major problems facing Egypt, including an economic crisis that is making it harder for the state to import fuel and food.