Al-Wafd Party candidate Numan Juma and al-Ghad Party candidate Ayman Nour are Mubarak's main contenders.
Ayman Nour, took 10%.
Nour charged that violations had marred voting and demanded re-elections.
But the election commission turned down the demand stating that the polling had been conducted impartially.
An election commission official said Nour's complaints had been investigated and had not been found true, including charges that bribes had been paid to secure votes.
The government had been vowing a clean vote, but Wednesday's election was marred by widespread reports of pressure and intimidation by the ruling party for voters to support Mubarak.
A key question was turnout. The number of voters might indicate how much Egyptians, apathetic by years of stagnation, are convinced by reform claims.
As polls closed, the government did not have turnout figures, but officials said large crowds had been seen at some polling stations.
Several independent monitoring groups said they expected turnout to be low and Ajazeera's correspondent also commented on low numbers heading to the polls.
Estimates released by the four-term president's main rival, Al-Ghad Party leader Ayman Nour, indicated that turnout stood at between 15 and 20% in rural areas and hovered between three and 5% in cities.
Indignant opposition candidates and independent monitors claimed on Thursday that incumbent Hosni Mubarak's camp had massively violated electoral laws during Egypt's first contested presidential poll.
Opposition candidates accuse the
NDP of violating electoral laws
Forced voting, paid voters, unmanned polling stations, missing indelible ink and the use of public transport to ferry voters to polling stations were only some of the accusations against Mubarak's National Democratic Party.
Independent monitors reported a litany of irregularities at polling stations, complaining they had been beaten, apprehended and interrogated by security services in several places.
Several rights groups said Mubarak supporters actively campaigned throughout the day and reported that some had voted on behalf of other people.
Interviewed on Aljazeera on Thursday, Al-Ghad Party's Nour said he would submit a report on what he called irregularities committed "to challenge the authenticity of the election results".
"The report concerns some incidents that have affected the will of the voters and other administrative issues that have violated constitutionally approved rules and procedures," he said.
Nour said he would hold a press conference on Friday where he would call for re-election in accordance with the legal Article 174, issued in 2005, to protest against the violations.
"These violations are related to the right of voters to cast their ballots in the context of the unified rules."
He said: "The committees have approved specific rules, but different ones were applied on Wednesday. In the evening, new rules were applied. This is a dangerous violation."
The government, for its part, played down reports of problems, saying they did not diminish what they called a major step towards democracy.
Mubarak (L) is expected to
easily win the election
"There may be some comments, maybe some violations happened, but we have to agree that we're seeing an experience that we can build on for a future that realises more freedom and more democracy in the Egyptian society," Information Minister Anas al-Fiqi said.
Government officials also voiced satisfaction with the polling process.
"The electoral process ... was as good as could have been envisioned," electoral commission secretary-general Osama Attawiya said.
There was no immediate comment from Mubarak's camp on the accusations, which sent a tense backdrop for what were guaranteed to be the beginning of a fifth term for the 77-year-old leader, whom observers had predicted would seek to tamper with the results to ensure sufficient legitimacy.
Speaking from Cairo on Thursday, Aljazeera's correspondent Abd al-Qadir Damish said many Egyptian voters had spoken of violations in different electoral constituencies.
Some said ballot boxes had been placed far away from observers in polling centres while others said judges were not to be found in the same room that housed the ballot boxes.
Nevertheless, Damish said, many citizens expressed satisfaction that a multi-candidate election had taken place for the first time, which was an improvement on the past, regardless of the near certainty about the winner of the political exercise.