After six decades under authoritarian military-backed rule, the 50million voters can decide whether to entrust the most populous Arab nation to an Islamist president for the next four years, as well as the Islamist-led assembly they chose earlier.

But secular candidates such as former Arab League chief Amr Moussa and Mubarak's last premier, Ahmed Shafiq, are in with a chance.

Some voters voiced disappointment at the performance of parliament, in which the Muslim Brotherhood's party has the biggest bloc. The assembly has been unable to assert itself over the government appointed by the generals who succeeded Mubarak.

Alarmed by rising crime, disorder and a failing economy, some Egyptians favour a man with government or military experience, even if he harks back to the Mubarak era.

Queues built up outside some polling stations in the baking sun, with many voters determined not to miss their chance to influence the first round. The government declared yesterday a public holiday to allow state employees to cast their vote.

If no one wins more than half the votes needed for outright victory, the top two will contest a run-off on June 16 and 17.

Unofficial first-round results might be known by tomorrow.

Khaled Abdou, 25, an engineer voting in Cairo said: "I must participate in choosing the president and I hope this leads to stability and change."

''This is the first time we can really choose our president and no one will mess with the result," said Ahmed Shaltout, a 36-year-old lawyer who said he would vote for Mursi.

Egyptians appear divided, even within families, between those willing to give Islamists a chance to rule this deeply conservative country and those who put security first.

"Security is the most important thing of course. If there is security we will have work, money and an economy. If there is no security no tourists will come. That's the first thing," said Sayed Mohamed, 33, a company manager, who supports Shafiq.

The next president will face huge tasks in reviving Egypt's wilting economy and restoring security. The sprawling police force, which virtually collapsed during the anti-Mubarak revolt, is only a shadow of its once-feared presence.