The reports were not immediately confirmed officially, although state newspaper al-Ahram said on its website that Ganzuri, an economist who served as Egyptian premier under ousted president Hosni Mubarak between 1996 and 1999, had agreed to lead a national salvation government.
The move if confirmed would mark the latest attempt by the Supreme Council of the Armed Forces (SCAF) to regain the initiative after days of deadly clashes since Saturday between security forces and protesters demanding an immediate end of military rule.
The clashes, in which at least 38 protesters have been killed and more than 2,000 injured, led to the resignation of caretaker premier Essam Sharaf's cabinet on Tuesday.
The call for new protests in Tahrir Square come despite an apology by the military rulers on Thursday for police killings.
The violence has cast a dark shadow over Monday's parliamentary elections, leading the SCAF to pledge to maintain security during the first poll since popular uprisings toppled Mubarak in February.
There was an uneasy calm on Thursday among the crowds massed in the square, the epicentre of Egypt's popular unrest, after a truce negotiated by Muslim clerics.
The cabinet said in a statement on Facebook that an agreement has been reached between security forces and protesters to halt the confrontations plaguing Egypt.
The military council said stepping down would amount to a "betrayal" of the Egyptian people.
"The people have entrusted us with a mission and if we abandon it now, it would be a betrayal of the people," senior SCAF member General Mukthar al-Mulla told a news conference.
"The armed forces do not want to stay in power. We want to put the wishes of the people above all else," he added.
Another senior SCAF member, Major General Mamduh Shahine, said there would be no delay to the legislative elections.
"We will not delay the elections. This is the final word. They will be conducted according to the original dates."
Mulla said the SCAF, the armed forces and the interior ministry would work together to guarantee the security of the elections.
Fresh clashes broke out in the Mediterranean city of Alexandria on Thursday between security forces and protestors, who threw rocks at them and chanted slogans denouncing police brutality, state news agency MENA reported.
In Tahrir Square, some demonstrators remained unequivocal in their demands for the military to go.
But many Egyptians are worried about the impact on the country of the standoff between the protesters and the army.
"If the military just steps down, there will be chaos. I mean, there is chaos now, so imagine what would happen if the military steps down," said Essam al-Arabi, whose sells leather handbags near Tahrir Square.
Standard and Poor's ratings agency said on Thursday that it had cut its long-term rating on Egypt, by one notch to 'B+' due to the deteriorating political and economic outlook.
"The downgrade reflects our opinion that Egypt's weak political and economic profile... has deteriorated further" following the latest clashes, S&P said.
Tantawi, Mubarak's long time defence minister now in charge of the country, tried to appease protesters and defuse Egypt's political crisis in a rare television speech on Tuesday.
But he was criticised for not making mention of the deaths at the hands of police.
The SCAF has vowed to investigate and prosecute all those behind the deaths, and to offer assistance to the families of the dead and injured.
The deaths prompted an unusually strongly worded statement from Al-Azhar, Sunni Islam's highest seat of learning, calling on police not to shoot at demonstrators.
Grand imam Sheikh Ahmed al-Tayyeb said that any dialogue "stained with blood is doomed and its fruit will be bitter."
Al-Azhar "calls on the police leadership to immediately issue orders not to point their weapons at demonstrators... no matter what the reasons," Tayyeb said in a message aired on state television.
UN High Commissioner for Human Rights Navi Pillay called the images coming out of Egypt "deeply shocking," and urged the authorities to end their "clearly excessive use of force" against protesters.
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