Egyptians have voted in a parliamentary election that could bring Islamists closer to power, though the army generals who took over from President Hosni Mubarak have yet to step aside.

The Muslim Brotherhood, expected to do well in the marathon vote whose first stage drew millions to the polls, said the new parliament should form a government, setting it at odds with the military council which has only just named a new prime minister.

The election for the lower house is due to be held over three phases, concluding in early January. Early election results were expected to trickle out on Wednesday.

State television broadcast live footage of the vote count across Egypt, which has not seen an election this free since army officers overthrew the monarchy in 1952.

Though the Brotherhood went into the polls stronger than nascent secular parties, analysts say it is hard to predict the outcome given that most of the electorate are casting their ballots for the first time.

Election monitors reported logistical hiccups and campaign violations during the poll but no serious violence.

The outcome of the election in one of the Middle East's most influential powers will help shape the future of a region convulsed by uprisings against decades of autocracy.

Though it did not start the Egyptian uprising, the Muslim Brotherhood has emerged as a major beneficiary of the revolt. The group is now eyeing a role in shaping the country's future.

The Freedom and Justice Party, the Brotherhood's political wing established earlier this year, said Egypt's new parliament should form the government.

A government that is not based on a parliamentary majority cannot conduct its work in practice, Mohamed Mursi told reporters during a tour of polling stations in the working class district of Shubra in Cairo.

Therefore we see that it is natural that the parliamentary majority in the coming parliament will be the one that forms the government, said Mursi, whose group was outlawed but tolerated under Mubarak, adding:

We see that it is better for it to be a coalition government built on a majority coalition in the parliament.

SCOPE FOR TENSION

It was only last week that the military council appointed Kamal al-Ganzouri, a 78-year-old veteran of the Mubarak era, to form a cabinet to replace the government of Essam Sharaf, which resigned in the face of protests against military rule.

A military council member said at the weekend the new parliament would not have the authority to dismiss Ganzouri's government or form a new one. Yet observers question whether the council will be able to resist the will of a chamber elected in a fair vote, especially if voting carries on smoothly.

A senior figure in the once-banned Muslim Brotherhood said its FJP had done well in the voting so far.

The Brotherhood party hopes to win 30 percent of parliament, Mohamed El-Beltagy told Reuters.

The leader of the ultra-conservative Salafi Islamist al-Nour Party, which hopes to siphon votes from the Brotherhood, said organisational failings meant his party had underperformed.

But he told Reuters the party still expected to win up to half of Alexandria's 24 seats in parliament and, nationwide, 70 to 75 of the assembly's 498 elected seats.

In one of the military's first reactions to the election's first phase, General Ismail Atman, a ruling army council member, was quoted by Al-Shorouk newspaper as saying the poll showed the irrelevance of protests demanding an end to military rule in Cairo's Tahrir Square and elsewhere.

The general said turnout would exceed more than 70 percent, though the Brotherhood's Mursi said indications showed a lower figure of 40 percent.

The success of the first phase has deflected criticism faced by the military council, which has been under pressure from street protesters over what they see as the generals' attempts to maintain power and privilege in the post-Mubarak era.

Last week was Egypt's most violent since Mubarak was ousted: 42 people were killed in clashes triggered by the protests against the council.

Unidentified youths hurled petrol bombs near the square late on Tuesday. A Reuters witness heard gunshots and the state news agency MENA said two protesters suffered eye wounds which may have been caused by shots from a pellet gun.

An organiser of the protest said the trouble started when an unidentified group tried to enter the square.

Many Egyptians were worried the elections would be bloody. But there has been little sign of the thugs who were a feature of the rigged elections of the Mubarak era.

U.N. Secretary-General Ban Ki-moon congratulated Egyptians on the first stage of the election and the generally calm and orderly manner in which voting took place, a statement from his office said.

Les Campbell, of the Washington-based National Democratic Institute, one of many groups monitoring the poll, said it was a fair guess that turnout would exceed 50 percent, far above the meagre showings in rigged Mubarak-era elections.

(Additional reporting by Marwa Awad in Alexandria, Shaimaa Fayed in Damietta and Tom Perry, Patrick Werr, Peter Millership and Edmund Blair in Cairo; Writing by Tom Perry; Editing by Peter Millership)