The top candidates condemned the decision and blamed each other but appealed to Africa's largest democracy for calm, while they rushed back to the capital to learn more about what went wrong.
The postponement was announced a mere five hours before the polls were to open. The decision is a costly one, and authorities now must decide what to do with already delivered voting materials in a tense atmosphere where some electoral facilities in recent days have been torched.
Some bitter voters in the capital, Abuja, and elsewhere who traveled home to cast their ballots said they could not afford to wait another seven days. They warned that election apathy could follow.
The party backing top opposition challenger Atiku Abubakar accused President Muhammadu Buhari's administration of "instigating this postponement" with the aim of ensuring a low turnout at the polls.
A calm-looking Abubakar, speaking to reporters outside his home in northern Adamawa state, said his party would decide on the way forward after an electoral commission briefing Saturday afternoon. A party spokesman in Delta state in the restive south said the commission "has destroyed the soul of Nigeria with this act."
Buhari said he was "deeply disappointed" after the electoral commission had "given assurances, day after day and almost hour after hour that they are in complete readiness for the elections. We and all our citizens believed them."
His statement appealed to Nigerians for calm during the "trying moment in our democratic journey" and stressed that his administration does not interfere in the commission's work.
One ruling party campaign director in Delta state, Goodnews Agbi, told The Associated Press it was better to give the commission time to conduct a credible vote instead of rushing into a sham vote "that the whole world will criticize later."
Commission chairman Mahmood Yakubu in the early-morning announcement said that "this was a difficult decision to take but necessary for successful delivery of the elections and the consolidation of our democracy."
Frustrated voters gathered in the capital. "I came all the way from my home to cast my vote this morning ... and then I got informed that the election has been canceled, so that is the reason why I am not happy, and I'm very, very angry," voter Yusuf Ibrahim said.
A civic group monitoring the election, the Situation Room, said the delay "has created needless tension and confusion" and called on political parties to avoid incitement and misinformation.
Nigeria postponed the previous presidential election in 2015 because of deadly insecurity in the northeast, which remains under threat from Islamic extremists.
More than 84 million voters in this country of some 190 million had been expected to head to the polls in what is seen as a close and heated race between Buhari and Abubakar, a billionaire former vice president.
Both have pledged to work for a peaceful election even as their supporters, including high-level officials, have caused alarm with vivid warnings against foreign interference and allegations of rigging.
When Buhari came to power in 2015 he made history with the first defeat of an incumbent president in an election hailed as one of the most transparent and untroubled ever in Nigeria, which has seen deadly post-vote violence in the past.
Now Buhari could become the second incumbent to be unseated. This election is a referendum on his record on insecurity, the economy and corruption, all of which he has been criticized by some Nigerians for doing too little too slowly.
Uguru reported from Ughelli, Nigeria. Associated Press photographer Jerome Delay in Kaduna, Nigeria, contributed.
Follow Africa news at https://twitter.com/AP—Africa