He himself had been granted "much more powers" than past premiers, said Ganzuri, who served as Mubarak's prime minister between 1996 and 1999.
In a later television address, Ganzuri said he would formalise his government "before the end of next week" and would allocate some portfolios to younger people.
The new government, he added, would move to restore security and relaunch the development of Egypt.
But protesters in the square quickly rejected his appointment, saying he was not the man to lead a transition to democracy.
"We do not want someone who has been selected by the military council, we want a civilian who was with us in Tahrir during the revolution, someone who has the confidence of the people," said one protester, Omar Abdel Mansur.
Hundreds of protesters in the square branched off to the nearby cabinet offices to block Ganzuri from entering the building, chanting "revolution" and "Ganzuri is a former regime leftover."
"The youth of Tahrir had proposed (several) names. None of them were chosen. We have the feeling nothing has changed" since a popular uprising ousted Mubarak in February, said Mohammed Khattab, 30.
"Our mistake in the (January-February) revolution was to think that we had only to topple Mubarak."
The protesters proposed a list of presidential candidates to form a civilian leadership council, including former UN nuclear watchdog chief Mohamed ElBaradei, a prominent dissident during Mubarak's rule.
They were bolstered earlier by an announcement that the grand imam of Al-Azhar, Sunni Islam's highest authority, had thrown his weight behind them.
"The grand imam (Sheikh Ahmed al-Tayyeb) backs you and is praying for your victory," senior aide Hassan Shafie told them during a visit to the square.
And the imam at the square who led tens of thousands of worshippers in prayer called on the ruling military to hand over power to a national salvation government.
Sheikh Mazhar Shahin said protesters would remain in the square until their demands were met.
"There is no option but a national salvation government with the powers of a president," he said.
ElBaradei, whose name has been widely touted to be part of a new salvation government, joined the protesters in the square on Friday.
The Tahrir protest was countered by a rival demonstration in a square about three kilometres (two miles) away, where more than 10,000 people gathered to show support for the military.
"Down with Tahrir" and "Yes to the military council," they chanted.
"I joined the protests against the former regime," said one of the protesters, Mohammed Abdelhamid. "But the people in Tahrir today don't represent all Egyptians."
The rallies came three days before the first parliamentary elections since Mubarak's ouster in February, which left the military in charge.
The military announced on Friday that voting would take place over two days, instead of one, in each of the election's three rounds.
Washington, a close ally of Egypt, called on Friday for quick transfer to civilian rule.
"We believe that the full transfer of power to a civilian government must take place in a just and inclusive manner that responds to the legitimate aspirations of the Egyptian people, as soon as possible," White House press secretary Jay Carney said in a statement.
"The United States strongly believes that the new Egyptian government must be empowered with real authority immediately," Carney said.
On Tuesday, the SCAF accepted the resignation of the caretaker cabinet headed by the once-popular Essam Sharaf, whose fall from grace was due to his perceived weakness in the face of the army.
The violence, in which at least 41 protesters have been killed -- 36 of them in Cairo -- and more than 3,000 injured since Saturday, was cited as one of the factors that led to the resignation of Sharaf's cabinet.
The SCAF has said repeatedly that it does not have political ambitions and plans to hand power to an elected civilian authority after presidential elections which are set to take place no later than the end of June 2012.
However, it insisted on Thursday that it would not bow to pressure from the protesters in Tahrir, saying they did not represent the whole country.
"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 reporters.
--------------------------------------------------------------------------------------