Egyptians have begun electing a president freely for the first time, choosing between a former general of the old guard and an Islamist who is running for God.

Many were perplexed and fearful of the future and there were signs that, as in last month's first round, millions would not vote.

The contest, pitting Hosni Mubarak's last PM Ahmed Shafik against Mohamed Morsy of the Muslim Brotherhood, is supposed to seal a democratic transition that began with the overthrow of Mubarak 16 months ago.

"We have to vote because these elections are historic," said Amr Omar, voting in Cairo.

Putting aside misgivings about the Brotherhood's religious agenda, he said: "I will vote for Morsy. Even if it means electing the hypocritical Islamists, we must break the vicious cycle of Mubarak's police state."

Many other Egyptians, weary of political turmoil and the economic crisis it has brought, believe Shafik has the backing of the "deep state" – entrenched interests from the military to big business – and so may be better placed to bring prosperity.

The election comes amid a constitutional crisis and a stand-off between the ruling generals and the Brotherhood, which emerged from decades of repression under Mubarak and previous military leaders to sweep the parliamentary vote.