The comments by Mr Carter, who heads a delegation of 60 US observers, were welcomed by his own team, US Republicans and the European Union's 100 monitors who until now have spoken only off the record of their concerns.
These concerns have included a claim that about 16 million voter registration cards have not been accounted for, and numerous reports of ballot box stuffing and inflated voter tallies, especially in the southern oil-producing states, where voting has also been marred by ethnic violence.
Mr Carter urged the two candidates in the election, Olusegun Obasanjo and Ola Falae, to urge their supporters to respect election regulations.
He also criticised the military regime for failing to publish a constitution ahead of the elections, which began at local authority level last December.
Ten days ago, the regime of General Abdulsalami Abubakar announced it had re-enacted the country's 1979 constitution. The move meant little to Nigerians who have not been informed of the future powers of the bodies they have been voting for, such as the House of Representatives.
Today's vote is to elect a president who will serve for four years as head of Nigeria's fourth republic since independence from Britain in 1960. In 39 years Nigeria has known civilian rule for only 10. The new president, who must gain at least 25 per cent of the votes in two-thirds of Nigeria's states, will formally take over on 29 May.
Since 1960 dictators and coups have succeeded one another, and statistics and election boundaries have been manipulated. That is not difficult, as Nigeria's real population could range from 90 to 128 million.
Sixty million ballots, printed in Britain and flown in on Thursday, are thought to be "about the right number" for the 57 million people who, in October, gave their names, ages and thumbprints to registration officers around the country.
The campaigns, which began after primaries held only two weeks ago, were dominated by pacts between powerful individuals rather than by issues.
But Abdul Oroh, director of the Civil Liberties Organisation, said: "This is the best we can do for the moment. We cannot expect elections organised by the military to be democratic. This is a step in the right direction."
Balarabe Musa, former governor of Kaduna state, said: "The system is such that only a thief can come to power in elections in Nigeria.
"The person who takes over in May will be among the richest and most corrupt of Nigerians."Reuse content