Egyptians are voting for the second day in the country's first free presidential elections - 15 months after Hosni Mubarak was ousted.
Queues were reported at some polling stations, and media reports said turnout was higher than on Wednesday.
The election pits Islamists against secularists, and revolutionaries against Mubarak-era ministers.
A row erupted between two of the main candidates for apparently spreading damaging rumours about each other.
In a BBC interview, Amr Moussa launched an angry attack on his rival Ahmed Shafiq and denied what he described as "sinister rumours" that he was about to withdraw from the race.
Mr Moussa and Mr Shafiq's campaigns have apparently been suggesting that the other is losing badly and is about to withdraw.
In all, 13 candidates are running. The front-runners are:
* Ahmed Shafiq, a former commander of the air force and briefly prime minister during February 2011 protests
* Amr Moussa, who has served as foreign minister and head of the Arab League
* Mohammed Mursi, who heads Muslim Brotherhood's Freedom and Justice Party
* Abdul Moneim Aboul Fotouh, an independent Islamist candidate
Mr Shafiq, Mr Fotouh and Mr Mursi have all been accused of breaking rules requiring candidates keep silent on polling days.
Voting has now been extended by an hour until 21:00.
The military council which assumed presidential power in February 2011 has promised a fair vote and civilian rule.
On Wednesday, there were large queues in many places, and voting passed off calmly for the most part.
However, protesters in Cairo threw shoes and stones at a convoy of Mr Shafiq, who was Mr Mubarak's last prime minister.
There were also reports that a group of female voters was denied access to a polling station in the capital because they were wearing a full face veil.
The US hailed the election, with State Department spokeswoman Victoria Nuland describing it as a "milestone" in Egypt's transition to democracy.
Fifty million people are eligible to vote, and preliminary results are expected over the weekend.
Until a new constitution is approved it is unclear what powers the president will have, prompting fears of friction with a military which seems determined to retain its powerful position.
'Elections under tanks'
Voting across the country resumed at 08:00 local time (06:00 GMT). The authorities have declared Thursday a holiday.
The BBC's Jon Leyne in Cairo says some Egyptians may have been waiting for a second day of voting to avoid crowds.
Local TV reporters in several locations said turnout was higher than on the first day.
But in Alexandria the opposite appeared to be true, and military police were seen driving around urging people to vote.
NGOs and rights groups monitoring the election have reported some complaints.
Egypt's National Council for Human Rights (NCHR) told the BBC it had received 50 complaints on electoral violations ranging from delay in opening voting booths, to campaigning for candidates outside polling stations during voting.
Meanwhile young people in Cairo told the BBC they had doubts about the vote.
"Has the revolution accomplished all of its goals? No," said Dina Kassem.
"You know we still have so much to go [sic] like any other country. The French revolution took how many years? But you can see the fact of it today. And that's what we're hoping to bring to Egypt."
Assia Krim was less hopeful.
"Everyone is disappointed after the revolution. Elections under a military regime are not elections. Elections under tanks, I'm sorry - they are not elections," she said.
Reassurance
Counting will begin as soon as polls close, and some individual polling stations are expected to announce their results by Friday morning.
The results will then be collated and announced in full on Tuesday. No clear picture is likely to emerge until then.
A run-off vote is scheduled for 16 and 17 June if no candidate manages to get more than 50% of the votes.
The Supreme Council of the Armed Forces (Scaf), worried about potential post-election unrest, has sought to reassure Egyptians that it will be the voters themselves who decide who will be the next president.
The Arab Spring began last year in Tunisia, inspiring pro-democracy activists across the Arab world.
Mr Mubarak, who was in power for three decades, resigned on 11 February 2011 after 18 days of protests in Cairo and other cities.
He is on trial for his alleged role in the deaths of protesters. A verdict is expected in June.
The period since he was forced from power have been turbulent, with continued violent protests and a deteriorating economy.
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