Thousands of these women have died because of lack of food in camps for internally displaced people in Nigeria's northeast after they were rescued from Boko Haram, Amnesty says.
Women interviewed by Amnesty said they were beaten and called "Boko Haram wives" by security officials whenever they complained about their treatment.
The report says that members of the Nigerian military and a local vigilante group Civilian Joint Task Force (Civilian JTF) "separated women from their husbands and confined them in remote 'satellite camps' where they were raped, sometimes in exchange for food."
Ten women in the Bama camp told Amnesty they were forced to date security officials to get food. One woman said a member of the JTF vigilante group raped her after he brought her food, telling her: "I gave you these things, if you want them, we have to be husband and wife."
"Sex in these highly coercive circumstances is always rape, even when physical force is not used, and Nigerian soldiers and civilian JTF members have been getting away it," Osai Ojigho, Director of Amnesty International Nigeria said.
"They act like they don't risk sanction, but the perpetrators and their superiors who have allowed this to go unchallenged have committed crimes under international law and must be held to account."
Deadly terror group
Boko Haram, described as the third deadliest terror group
by the Global Terrorism Index, has unleashed waves of brutal attacks across parts of northern Nigeria, bombing schools, churches and mosques and kidnapping women and children in a conflict that spans nearly a decade.
The conflict has killed thousands of people and also internally displaced two million people, according to the Internal Displacement Monitoring Centre.
However, the Nigerian army claims it has technically defeated Boko Haram and retaken territories seized by the militant group in the northeast.
Members of its troops recently rescued 1,000 hostages,
mostly women and children, from the militant's camps in Borno State, it said.
Hundreds of women along with their children have been held in overcrowded centers in northern Nigeria since 2015.
Amnesty said it had collected evidence that thousands of people have starved to death in displacement camps since 2015.
In the report, the women alleged that 15 to 30 people died each day between 2015 and 2016 due to lack of food in these camps.
The human rights group said satellite images of an expanding graveyard in one of the camps during the time confirmed their testimonies.
In a 2016 report
, another rights group, Human Rights Watch, said it had documented 43 cases of sexual violence against women by soldiers in displacement camps in northern Nigeria, forcing the Nigeria government to investigate.
Nigerian army spokesman John Agim denied the allegations in the Amnesty report, branding them "propaganda."
He said the army hasn't been deployed to displacement camps, which he said are run by the police, local vigilante groups and NGOs. "I wonder where Amnesty interviewed women who said they saw soldiers in these camps hoarding food and raping women?" Agim asked.
Agim accused the human rights group of republishing claims that had been investigated by the Nigerian government and had been found to be false.
"Amnesty wrote the same allegations in a report in 2015 and it was investigated then and found not to be true. Why are they presenting them in 2018 after investigations? It is all propaganda and when they continue to propagate these reports, it assumes the property of truth when its not refuted," Agim told CNN.
"Amnesty does not want our war against terrorism to finish; the Nigerian military maintains this position," he said. "Their reports on human right violations is to stop the selling of weapons to the Nigerian military by the American government and others and that approach is not working."
"The Nigerian army just rescued 1,000 Boko Haram captives, that is a good development, why is it not reflected in the report if they are being fair?" Agim added.
For it's part, Amnesty said there has been "no tangible action to address the problem and no one appeared to have been brought to justice," despite promises by the Nigerian government to investigate reports of alleged abuse in these camps since 2015.
"It is absolutely shocking that people who had already suffered so much under Boko Haram have been condemned to further horrendous abuse by the Nigerian military," Amnesty's Ojigho, said.
The organization called on the Nigerian government to make public the findings from a panel investigating the military's compliance with human rights provisions set up by Vice President Yemi Osibanjo.
Many women had testified before the panel whose report was submitted to Nigeria's President Muhammadu Buhari in February, the human rights group said.
"Now is the time for President Buhari to demonstrate his frequently expressed commitment to protect the human rights of displaced people in north-east Nigeria. The only way to end these horrific violations is by ending the climate of impunity in the region and ensuring that no one can get away with rape or murder," Ojigho added.
"The Nigerian authorities must investigate or make public their previous investigations on war crimes and crimes against humanity in the northeast," she added.
The Nigerian government told CNN the military had found cases of abuse in these camps during the period mentioned in Amnesty's report in 2015, countering the army spokesman's claims that the allegations were investigated and found not to be true.
"Over this period of time, the Nigerian military had indeed established cases of abuse and punishments meted out from orderly room trials and court martials that included the losses of rank, dismissals, and trials and convictions by civil courts," Garba Shehu, a spokesman for the president, told CNN.
However, Shehu echoed the Army spokesman's claims and accused Amnesty of "recycling" claims from a previous report.
Amnesty's report lacked "credibility, falling vehemently short of evidential narration," from victims by failing to address mechanisms put in place by the military and the president's panel after similar allegations were published in 2015, he said.
The Nigerian government was committed to investigating "all documented cases of human rights abuses," Shehu added.