But his ideas seemed to run counter to a suggestion by the prime minister to dissolve the Islamist organisation, the target of a fierce crackdown by the army-backed government last week.
The authorities declared a state of emergency and killed hundreds of people in raids on Wednesday on protest camps set up in Cairo to demand deposed president Mohamed Morsi's reinstatement.
The capital's frenetic streets, unusually empty in the past few days, were returning to normal on Sunday, although the army kept several big squares closed and enforced a curfew overnight.
At night, soldiers standing beside armoured personnel carriers man checkpoints, and vigilantes inspect cars for weapons.
Banks and the stock market reopened for the first time since Wednesday's carnage, with shares rapidly falling 2.5%.
"As long as we have bloodshed on the streets, it takes away any reason for foreign and regional investors to buy in Egypt," said Amer Khan, director at Shuaa Asset Management in Dubai.
The initiative by Deputy Prime Minister Ziad Bahaa el-Din, a liberal, calls for an immediate end to the state of emergency, political participation for all parties and guarantees of human rights, including the right to free assembly.
The Brotherhood has said it will keep up mass protests until Morsi, toppled by the army on July 3 after huge demonstrations against him, is freed from jail and returned to office.
It was not clear how much support Bahaa el-Din's proposal, seen by Reuters, could gain among the new leaders of a deeply polarised Arab republic experiencing the worst bout of bloodshed and internecine conflict in its six-decade history.
Blaming a defiant Brotherhood for the bloodletting, Prime Minister Hazem el-Beblawi has proposed banning the 85-year-old movement and effectively forcing it underground.
"There will be no reconciliation with those whose hands have been stained with blood and who turned weapons against the state and its institutions," Beblawi told reporters on Saturday.
Bahaa el-Din stayed in office even after a leading fellow-liberal, Deputy President Mohamed ElBaradei, resigned over the violent break-up of the protest camps in Cairo on Wednesday.
His proposal does not address Morsi's fate or specifically call for an amnesty for detained leaders of the Brotherhood.
The Islamist organisation, which won five successive votes held in Egypt since the fall of president Hosni Mubarak in 2011, now faces the prospect of political elimination by army-backed rulers who say the most populous Arab nation is at war with "terrorism".
During Morsi's year in power, accusations of incompetence and attempts to monopolise government tarnished the reputation the Brotherhood had acquired for social work and upholding Islamic principles in 30 years of opposition to Mubarak.
Brotherhood leaders accuse the military of deliberately sabotaging their time in office and plotting their demise.
More than 700 people have died, most of them backers of Morsi, in four days of violence. That has earned Egypt stiff condemnation from Western nations, uncomfortable with Islamist rule but also with the overthrow of an elected government.
EU to review relations
European Council President Herman Van Rompuy and European Commission President Jose Manuel Barroso called on all sides to show restraint and prevent further violence, saying the EU would "urgently review in the coming days its relations with Egypt and adopt measures aimed at pursuing these goals".
The crackdown has, however, drawn messages of support from wealthy Arab allies such as Saudi Arabia, which have long feared the spread of Brotherhood ideology to the Gulf monarchies.
UN Secretary-General Ban Ki-moon condemned attacks on churches, hospitals and other facilities, saying the authorities and politicians shared responsibility for ending the violence.
Clashes flared briefly on Saturday when Morsi supporters exchanged fire with security forces in a central Cairo mosque, where scores of Muslim Brotherhood protesters had sought refuge from confrontations with police the day before.
Police finally cleared the building and made a string of arrests, with crowds on the street cheering them on and harassing foreign reporters trying to cover the scene.
"We as Egyptians feel deep bitterness towards coverage of the events in Egypt," presidential political adviser Mostafa Hegazy said, accusing Western media of ignoring attacks on police and the destruction of churches blamed on Islamists.
After two pro-Morsi protest camps were crushed by police on Wednesday, the Brotherhood launched a "Day of Rage" on Friday, when at least 173 people were killed in clashes. Police have since arrested more than 1 000 Brotherhood "elements", the Interior Ministry said. The state news agency said 250 faced possible charges of murder, attempted murder or terrorism.
The Brotherhood has called for daily street protests this week, but there were no reports of trouble on Sunday morning. – Reuters