Cairo (CNN) -- Tahrir Square was peaceful Wednesday as Egyptians awaited initial results of parliamentary elections, a break from the clashes that have gripped Cairo for much of the past two weeks.
The Muslim Brotherhood and the Al Noor Salafi Muslim Party claimed a lead in ballot counting, but no official results were expected until Thursday at the earliest.
Voting took place Monday and Tuesday, the first elections since President Hosni Mubarak was overthrown in February.
It is the first time some Egyptians -- young and old -- have ever cast ballots. Citizens are picking members of the lower house of parliament, which will be tasked with drafting a new constitution after three decades of Mubarak's rule.
Some voters and human rights activists expressed hope that their votes will actually count, though some boycotted the elections saying they don't trust the voting will be free and fair.
There were reports of some illegal campaigning taking place.
Ali Al Dali, an official monitor for the Egyptian Association of Human Rights, said eight cases of vote-buying had been documented in Alexandria, and police had been notified. About 45% of eligible voters in the city had cast ballots, he said.
By nightfall Tuesday night, new clashes erupted in Tahrir Square. The unrest stretched into early Wednesday.
At least 88 people were hurt, 28 of them seriously enough to go to a hospital, a Health Ministry official, Dr. Adel Adawi, told the state-run newspaper Al-Ahram. The rest were treated at makeshift clinics in the square, Adawi said, but hospitals expected more people to be brought in.
The victims were hit by rocks, glass bottles, birdshot and Molotov cocktails, Dr. Hisham Shiha, another Health Ministry official, told CNN. At least a dozen gunshots rang out across the plaza, and ambulances darted in and out of the square as the fighting continued.
Tahrir Square was the epicenter of the protests that drove Mubarak from power and the demonstrations in recent days against the military council that succeeded him.
Witnesses said Tuesday's melee began with fights between vendors and protesters who threw rocks and attacked their kiosks with sticks. The protesters complained some vendors were giving demonstrations a bad image by selling marijuana, said Mina Hagras, one of the demonstrators who has been camped in the square.
"This is not the spirit of the revolutionaries or the square," Hagras said. "They warned them. They did not stop. So they took matters in their own hands and beat them up. Now, state TV is saying all the protesters in (the) square are thugs and drug users. This is not fair."
But Mohamed Shafei, whose sandwich stand was destroyed in the brawl, said the protesters turned on the vendors indiscriminately and confiscating their goods.
"Yes, there were several vendors selling hashish and pills, but not all of us are the same," Shafei said as he carried the remains of his kiosk. He added that the vendors were "retaliating."
Elections for Egypt's lower house of parliament are scheduled to take place in three stages, based on geography. The last of the three stages is set to take place in January.
Upper house elections will run between January and March.
Presidential elections will be held by June, according to the Supreme Council of the Armed Forces, Egypt's acting ruling body. Military leaders have said they will hand over power to a new government when one is elected, but many Egyptians say they don't trust the council and fear the military will cling to power.
Over the past two weeks, at least 42 people have been killed in clashes as protesters called for an immediate end to military rule. An additional 3,250 have been wounded, according to the Health Ministry.
CNN's Ben Wedeman, James Partington, Ivan Watson, Leone Lakhani and Jim Clancy and journalists Mohamed Fadel Fahmy and Ian Lee contributed to this report.