The coalition said its call is directed to other national political forces, as well as the military and the interim government it supports. The coalition offered a two-week period for them to discuss the proposal.
While the proposal offered Saturday doesn't call for Morsi's return to the presidency, it insists on basing a solution on "constitutional legitimacy." The group didn't elaborate.
A spokesman for the Brotherhood and its political party said one way of restoring constitutional legitimacy is to re-install Morsi briefly, so he can call for new elections or name a new prime minister. The spokesman spoke on condition of anonymity because he was not authorized to speak to journalists about the proposal.
It's unclear how the coalition proposal would fit into a military-backed plan already in place for returning Egypt to democracy. That plan calls for a referendum by the end of the year on changes to the Islamist-drafted constitution. That would be followed by parliamentary and presidential elections by summer.
Deputy Prime Minister Hossam Eissa told The Associated Press that Morsi supporters should accept the military-backed plan first as a starting point for talks.
"A call for dialogue has to be based on accepting the accomplishments (since Morsi's ouster) and the current arrangements," Eissa said. "With no acceptance, there is no dialogue."
Meanwhile, a panel of judges told a court in Egypt it should disband the Brotherhood's political arm, the Freedom and Justice Party, and seize all its assets, state news agency MENA reported. A report by the panel said the party should be dissolved as another court order already banned the Brotherhood, the agency said.
The panel offered its opinion as guidance for the court, which is expected to rule on whether to disband the party in February.
MENA also reported that the panel offering amendments to the constitution should have a final draft of its recommendations ready by either Tuesday or Wednesday. Members of the Islamist coalition have criticized the work of the panel.
"The initial stance for the coalition is that we refuse whatever results a non-elected authority comes up with," Yousri Hamad, the vice president of the ultraconservative Salafi party, told the AP.
Magdy Salem, vice president of the Islamist Party, the political arm of the former militant group Islamic Jihad, said the coalition wants the solution based on the 2012 Islamist-drafted constitution.
Also Saturday, U.S. Defense Secretary Chuck Hagel spoke on the telephone with Egypt's military chief, Gen. Abdel-Fatah el-Sissi, who led the coup that ousted Morsi.
Assistant Press Secretary Carl Woog said in a statement that Hagel welcomed the end of Egypt's three-month period of emergency law and curfew, and reiterated that the United States values its ties with Egypt as well as freedom of expression.
"The leaders also discussed the importance of continuing progress on the roadmap toward inclusive democracy," Woog said.
