The MDP has said that hundreds of voters have been unjustly dropped from voter lists, but said they were satisfied with the overall turnout among the 209,000 people eligible to vote.
Gayoom, who leads the Dhivehi Rahyithunge Party (DRP), took 40 per cent of the votes in the first round, but was short of the majority he needed to win.
Nasheed, a former political prisoner and outspoken critic of the president, came in second with 25 per cent of the first-round vote.
Hussein Iqbal, a hotel employee, said he spent an hour in line to vote "for change".
Ibrahim Shahib, a private sector employee, said he voted for Gayoom, who "may not be great, but still he is the better candidate".
Gayoom and Nasheed both say that they are confident of victory in the second round.
Stephanie Scawen, Al Jazeera's correspondent reporting from Male, said: "Several of the candidates who dropped out after the first round have said they will support Nasheed.
|Gayoom has concentrated his campaign on the Maldives' outlying atolls [AFP]
"This is the first ever multi-party presidential election.
"While president Gayoom may have been in power for 30 years, and expected to win the first round outright, he only got 40 per cent of the vote. That was 10 per cent short of the 50 per cent he needed, so it has gone into a run-off.
"The president is counting on support from women and the older electorate. But the young people said they want change, they would rather see anyone in power than Gayoom," she said.
Gayoom has presided over the Maldives since 1978, but he faces a tough challenge in the run-off after Hassan Saeed, the former attorney-general who came in third, threw his support behind Nasheed.
Nasheed has been in and out of jail, once being held for three years, and was described by Amnesty International as a "prisoner of conscience".
"Gayoom had the opportunity to gracefully bow out and allow the reforms to go ahead," Nasheed told the AFP news agency on Monday.
"My appeal is for him to allow a peaceful transition," he said before the final round.
Gayoom declined to speak to reporters on Tuesday, but later told the AFP news agency that he did not want to comment, fearing it might be "misinterpreted as an election law violation."
Vote 'for change'
Nasheed has concentrated his campaign in Male, while Gayoom has toured the country's outlying atolls in an attempt to secure support from conservative voters.
Gayoom has been praised for helping bring major development to this small nation of 1,190 coral islands but, although the nation is the richest per head of population in south Asia, it faces a housing shortage, rising crime and drug abuse.
The president has said that he is the only individual who can implement changes across the country, while opposition parties say he has used corruption and strong-arm tactics to maintain his rule.
Gayoom has survived at least three coup attempts.
The Maldives, a Sunni Muslim nation of 300,000 people, has never held multi-party elections before.
Preliminary results will be released by Wednesday and the official count will be known within the next five to six days, according to the election commission.