Critics say the truce proposal reflects cracks within the Islamist alliance led by the Brotherhood, with much of its leadership either imprisoned or on the run.
"They want to lift pressure on their groups and jump off the Muslim Brotherhood boat that is sinking right now," said veteran journalist and analyst Makram Mohammed Ahmed. "Everyone is searching for a way out, but this is too late."
Morsi supporters previously have insisted on the reversal of three moves by the military: Morsi's return to power, the lifting of the suspension of Islamist-drafted constitution and the restoration of the only legislative council under Morsi, as three preconditions to talks.
But Islamic Jihad leader Mohammed Abu Samra told The Associated Press that the proposed truce has no "red lines."
"We are paving the way for talks," Abu Samra said by telephone. "We can't hold talks while we are at the points of swords in the midst of killings and crackdowns." He said the groups were "extending their hands" to avoid a bloodier confrontation with the military, which he accuses of "defaming" the Brotherhood in the media and mosques.
Asked about Morsi's return to power, he said, "Blood is more treasured than seats of power ... we are no longer upholding return of the constitutional legitimacy."
Top Brotherhood negotiator Amr Darrag also said his group is open to talks but needs "confidence-building measures," such as an investigation into the killings of hundreds of Morsi supporters during the past month. But, he added, "The other side didn't show a single gesture or any sign that it is ready for dialogue. It only talks about it."
The interim president's office could not immediately be reached for comment. But on Saturday, Egypt's Interim Prime Minister Hazem el-Beblawi told reporters that security measures will not be enough on their own and that Egypt "must go down the political path" to work out a democratic transition through reconciliation.
He ruled out talks with anyone who had committed acts of violence.
Members of the Brotherhood lashed out after Morsi's July 3 ouster in a military coup, which came as millions of Egyptians called on him to step down because of his alleged abuse of power.
The current bout of violence was set off when security forces backed by snipers and armored vehicles broke up two sprawling pro-Morsi protest camps on Aug. 14. More than 1,000 people, most Morsi supporters, were killed in the raids and other violence over the next several days. Morsi's supporters retaliated by attacking dozens of police stations, torching churches and government buildings.
Authorities declared a state of emergency and imposed a curfew in Cairo and several other areas to try to quell the violence.
The crackdown continued Monday, as the state news agency announced the arrest of former youth minister and senior Brotherhood member Osama Yassin. Several of the group's leaders are still on the run. The Brotherhood has lost much public support and is now largely resented by the general population. Its offices and Brotherhood-owned businesses have been attacked, while Egypt's media almost uniformly against it since the closure of Islamist TV stations describes the group as "terrorist."