Cairo (CNN) -- Thousands of Egyptians gathered in Cairo's Tahrir Square Tuesday night to protest what they call a coup by Egypt's military rulers and show their support for the Muslim Brotherhood presidential candidate. 

Conflicting reports about the health of ousted President Hosni Mubarak overshadowed the protest, as one news agency reported he was clinically dead, which the military quickly denied. 

"He is not clinically dead as reported, but his health is deteriorating and he is in critical condition," Gen. Mamdouh Shahin, a member of the Supreme Council of the Armed Forces, told CNN. 

Conflicting reports about whether Mubarak has died 

"They're playing with us," one Tahrir Square demonstrator said. "All of the sudden, all of this? If he's really dead, it's God's will. I would hope he lives to see the new president." 

Both candidates in what the United States called Egypt's "historic" presidential runoff over the weekend are claiming victory, the latest twist in the country's chaotic political upheaval. 

A spokesman for Ahmed Shafik -- the last prime minister to serve under Mubarak -- said Tuesday that Shafik had won, state-run Nile TV reported. 

At a news conference, Mahmoud Abu Baraka said the campaign was certain it had the correct numbers. 

Mohamed Morsi, the Muslim Brotherhood candidate, claimed victory Monday and vowed to build an inclusive government. "No one's rights will be left out of it, and no one will dominate over the other," he said. 

Egypt has not announced an official result. 

The dueling announcements come amid questions over just how much authority the president will even have in the new Egypt. The Supreme Council of the Armed Forces, which has run Egypt since Mubarak's ouster, stripped the position of much of its power. 
Does his opponent agree?
A spokesman for Ahmed Shafik -- the last prime minister to serve under Mubarak -- said Tuesday that Shafik had won