Egypt's powerful Muslim Brotherhood says the high turnout for parliamentary elections indicates a popular demand for civilian control, challenging the country's military rulers as Islamist parties prepared to dominate the freest polls in living memory.

Media reports indicate the Brotherhood's Freedom and Justice party has secured more than 40 percent of the vote after counting so far. Ultra-conservative Salafist groups also are expected to score major gains in Egypt's second city, Alexandria.

Partial results are expected later Wednesday, with runoff votes for some parliamentary seats to be held next week. Full tallies for the lower house will not be announced until January, after two more rounds of voting in the rest of the country. The entire election will not be over until March.

Authorities said turnout likely exceeded 70 percent in the nine of 27 Egyptian provinces that have voted so far in the first elections since a popular uprising forced President Hosni Mubarak to resign in February.

Freedom and Justice party leaders said Egypt's new parliamentary majority should form the next government and choose the prime minister. They said the high turnout Monday and Tuesday showed that voters want parliament to have that power, not the generals.

But Egypt's ruling military council has said the newly elected legislature would not have the authority to dismiss their latest appointment, Prime Minister Kamal el-Ganzouri, or his government.

The embattled military chiefs hailed round one as a success, claiming the high turnout meant protesters camped in Cairo's Tahrir Square and those demonstrating elsewhere do not represent most Egyptians.

Security officials said about 80 people were hurt late Tuesday when clashes erupted between angry street venders and activists who attempted to evict them from the square. The masses that once demonstrated in Tahrir have dwindled to a few thousand and talks are underway among youth groups to leave the area.

Many Egyptians were worried the elections would see widespread violence between rival supporters. Instead, the vote won international praise.

U.N. Secretary General Ban Ki-moon congratulated Egyptians for what he called their enthusiastic participation at the ballot box. U.S. State Department spokesman Mark Toner calls the voting peaceful and a success.

But the chief of Egypt's National Human Rights Council, Hazem Mounir, said the voting process is confusing, blaming it on what he called a weak legal framework for elections and no independent election commission.

Nine days of clashes between protesters and police leading up to the elections killed 42 people and left more than 3,000 injured.

The historic elections will determine whether Egypt moves down a more Islamic path after nearly 60 years as an authoritarian secular state essentially run by the military.