Nigerians turned out in large numbers Saturday to vote for a president as Africa's most populous nation sought to make history by holding its cleanest polls for head of state in nearly two decades.

Voting was generally calm in most of the country, though two explosions hit the northeastern city of Maiduguri late Friday and early Saturday, with no casualties reported.

The same city was hit by two blasts during parliamentary polls last week.

Polling stations across the country opened on time, and even earlier in some areas where large numbers of enthusiastic voters turned up and spoke of wanting to participate in a historic occasion in a country weary of flawed ballots.

President Goodluck Jonathan, the clear favourite in the election, voted in his home state of Bayelsa in the oil-producing Niger Delta region, saying he was fulfilling his pledge not to interfere in the ballot.

"Nigeria is now experiencing a true democracy, where we the politicians have to go to the people," he said. "People have shown the highest degree of interest, so you can describe it as a new dawn in our political evolution."

Long lines formed at polling stations in and around the capital Abuja.

"There is no more rigging," said Eghosa Osaguona, a 46-year-old trader at an Abuja polling unit. "More and more people are aware of their rights."

Jonathan has staked his reputation on the conduct of the polls, repeatedly promising a fair election in the continent's largest oil producer long held back by corruption and with a history of vote fraud and violence.

His main challenger is ex-military ruler Muhammadu Buhari, who benefits from significant support in the country's north and has developed a reputation as an anti-graft figure, though his regime in the 1980s was also accused of outrageous rights abuses.

A crowd of hundreds loudly cheered him as he arrived to vote in the northern city of Daura, alleging there had been cases of fraud.

"We are still receiving reports of electoral fraud, of ballot stuffing in some places, but people are going to (electoral commission) offices to lodge complaints," he told journalists.

An enormous effort has been undertaken to hold a credible vote, but violence poses a risk, with bomb blasts and other attacks having killed dozens in the run-up to polls, including during last week's parliamentary ballot.

Tremendous hopes have been placed in the recently appointed head of the electoral commission, Attahiru Jega, a respected academic who ordered a series of reforms. More than 73 million people registered to vote.

But in an example of how difficult bringing about such change in Nigeria can be, a first attempt at holding parliamentary polls on April 2 had to be called off when material and personnel failed to arrive in many areas.

When the parliamentary poll finally did go forward on April 9, officials and observers described it as a significant step forward for the country.

There has been clear enthusiasm among voters to cast ballots, and a number stayed behind in some areas last week to record the counting process on mobile phones. Clips of vote counting were posted on YouTube.

The ruling Peoples Democratic Party lost ground in last weekend's parliamentary vote, and opposition parties restarted negotiations this week in a bid to team up against Jonathan.

But those talks collapsed, leaving the opposition with a difficult path to unseat an incumbent running for a party that has won every presidential poll since Nigeria returned to civilian rule in 1999.

Jonathan, 53 and a southern Christian, is the first president from the Niger Delta region.

He had an almost accidental rise to power that culminated with him being thrust into office last year following the death of his predecessor, Umaru Yar'Adua.

His calm approach has led some to call him weak, while others say it is better suited to bringing about change in Nigeria, a nation of some 250 ethnic groups and a population roughly split between Christians and Muslims.

Buhari, 69, is a northern Muslim who has run for president twice before. Many in the north see him as an opportunity to return power to their economically marginalised region.

There are two other main candidates in the race: Nuhu Ribadu, the former head of the country's anti-graft agency, and Ibrahim Shekarau, governor of the northern state of Kano.