Ordinary citizens, opposition party members and private groups monitoring the vote told The Associated Press on Wednesday that election workers inside polls in Luxor instructed voters to choose Mubarak, who is expected to be easily re-elected to a fifth six-year term.
In Alexandria, workers for the ruling National Democratic Party promised food to those who cast a ballot, voters said.
Polling officially closed at 10:00pm (1900 GMT) on Wednesday, state television and AFP correspondents said. The country's 9865 polling stations had opened at 8:00am (0500 GMT). Official results are not expected before Thursday night.
More than 3000 people marched through downtown Cairo at midafternoon - by far the largest crowd drawn by the opposition group Kifaya, or "Enough" in Arabic.
Police watched from a distance, despite government vows the day before that protests would not be allowed.
Egypt says the decision to allow challengers to Mubarak signals a move towards greater democracy in a country that has seen authoritarian rule for more than a half-century.
Opponents say Mubarak's party
controls the electoral process
Opponents, however, dismissed the reform claims as a sham.
They note that Mubarak's party controls most of the government, including the electoral process.
They argue the wide publicity given Mubarak by state-owned media made it difficult for opponents to gain notice.
The leading opposition candidate, Ayman Nour, said that the
elections "are not fair at all" and that he knew of instances where voters were bribed.
He told a late-afternoon news conference: "We accept only the results of free and fair elections, and we won't accept results of rigged elections."
But a spokesman for the election commission, Osama Atawaya, said the commission had received no complaints of voter bribery.
He defended the fairness of the vote overall and predicted turnout would be high.
Reporters, however, said turnout among the 32.5 million Egyptians registered to vote appeared light at many polling stations, although voting was likely to increase after work hours.
Many are deeply alienated from a government they see as accomplishing little and believe the election will not make a difference.
Until now, the 77-year-old Mubarak has been re-elected in referendums in which he was the only candidate and voters' only option was saying "yes" or "no" to his continuing in power.
Mubarak has promised further democratic steps if re-elected.
Ayman Nour said bribery is rife
and elections "are not fair at all"
Accountant Ahmad Ibrahim al-Shimi, 41, was one of many who joined the Kifaya march that started at noon in Cairo's main square, then swelled and spread to surrounding streets.
"I've never been in a demonstration before, I've never done anything before. But I'm disgusted. I've had enough," he said.
Many ordinary Egyptians say what they really hope for is change without disruption, crisis or violence, leading to better jobs and more opportunities in the economically stagnant country of 72 million people.
Others seem to genuinely fear change and said they would freely vote for Mubarak, long seen as the nation's father and protector.
"I can't take a risk at a time like this because this is the destiny of a country," said Mohammad Shahat Bilal, a 58-year-old welder in Alexandria. "We don't want what happened in Iraq to happen here. We want a stable country."
Nine candidates are running against Mubarak, but only two are considered significant: Nour of the al-Ghad Party and Numan Gumaa of the Wafd, the oldest opposition party.
"I've never been in a demonstration before, I've never done anything before. But I'm disgusted. I've had enough"
Ahmad Ibrahim al-Shimi,
Nour, a young, media-savvy candidate whose arrest earlier this year raised international protests, said before the vote that he hoped elections would be "conducted with transparency. And if this happens it will be a big achievement for Egypt."
Mubarak was among the first to vote, casting his ballot in a school close to the presidential palace, accompanied by his wife and son Gamal, a rising politician.
The country's election commission said on Wednesday that private groups and observers were welcome to go inside polling stations, despite earlier rulings that only voters, judicial supervisors, election workers and some party representatives could enter.
There were many charges of election fraud.
In Luxor in the south, university student Ahmed Mohammed Ahmed Ali said he was shocked when an employee inside a polling station told him he should vote for Mubarak or no one.
Ali said he refused and insisted on voting by himself.
He would not say whom he chose.
Two women interviewed by an AP reporter in the northern city of Alexandria said a ruling-party official had brought them to the polls in a bus and given them voter-registration cards, even though neither had ever registered.
One of them, Sohar Ahmed Ali, 37, wearing a full-length black cloak and veil, said she voted for Nour.
"It is a personal freedom," she said defiantly. "No one looks after the youth."
The other woman, Amnah Mohammed, 35, said she voted for Mubarak and planned to go collect the food, oil and sugar packet that a ruling-party member had promised her if she voted - a violation of the law.
"What would be the guarantee that anyone else will do anything for us?" she asked.
In Luxor, Wafd Party representative Shaaban Haridi Bakr said he told a judge supervising a polling place that one election employee wrote on a ballot rather than the voter himself.
Bakr said the judge yelled at the employee, but Bakr asserted that the employee went back and continued the same fraud.
Judges are supposed to independently monitor the voting, but critics contend that many of them are low-level officials and thus vulnerable to pressure by the ruling party.
Past parliamentary elections have been marred by widespread reports of vote-rigging.
Final result by Saturday
In a 25 May referendum that set up Wednesday's vote, the official turnout was 54%, but judges who supervised the polling stations denied that figure and said the turnout did not exceed 3%.
There also have been several instances of police and ruling-party violence against opposition demonstrators this year, including during the May referendum.
Final results were not expected until Saturday.