The human rights group says it was told by credible sources that the military had more than four hours’ warning of the raid by Boko Haram militants.
Fifty-three of the girls escaped soon after being seized in Chibok on April 14 but more than 200 remain captive.
Nigeria’s authorities say they “doubt the veracity” of the Amnesty report.
Nigerian President Goodluck Jonathan said on Friday that he believed the schoolgirls were still in his country and had not been moved to neighboring Cameroon.
“There are stories that they have moved them outside of the country. But if they move that number of girls to Cameroon, people will see, so I believe they are still in Nigeria,” Goodluck Jonathan told journalists at a meeting of the World Economic Forum in Abuja.
Amnesty International says it was told by several people that the military in Maiduguri, capital of the north-eastern Borno state, was informed of the impending attack on Chibok town soon after 19:00 local time.
It says that a local official was contacted by herdsmen who said that armed men had asked them where the Government Girls’ Secondary School was located in the town.
Despite the warning, reinforcements were not sent to help protect the town in the remote area, which was attacked at around midnight, Amnesty International says.
One reason, the rights group says, was a “reported fear of engaging with the often better-equipped armed groups”.
Amnesty’s Africa Director Netsanet Belay said it amounted to a “gross dereliction of Nigeria’s duty to protect civilians”.
Boko Haram has admitted capturing the girls, saying they should not have been in school and should get married instead.
In a video released earlier this week, leader Abubakar Shekau threatened to “sell” the students.
Teams of experts from the US and UK – including military advisers, negotiators and counselors – have arrived in Nigeria to help locate and rescue the abductees.
Seven American military officials arrived on Friday, with more expected to come on Saturday, including three FBI personnel.
Boko Haram, whose name means “Western education is forbidden” in the Hausa language, began its insurgency in Borno state in 2009.
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