The report alleged that police were using rape "as a means of torture to extract confessions from suspects in custody".
The group documented cases of mothers being raped by soldiers in front of their husbands and children and toddlers assaulted after their parents had been arrested.
Indictment
Kolawole Olaniyan, Africa director at Amnesty International, said: "The harsh reality is that, if you are a woman or a girl in Nigeria who has suffered the terrible experience of being raped, your suffering is likely to be met with intimidation by the police, indifference from the state and the knowledge that the perpetrator is unlikely to ever face justice."
Only a few policemen and no members of the armed forces have been convicted, Amnesty said, adding that without drastic reforms, security agents would continue to enjoy almost "complete immunity".
"Rape by police and security forces is endemic in Nigeria as the abject failure of the Nigerian authorities to bring perpetrators to justice," Amnesty oifficials said in presenting the 40-page report, entitled "Nigeria: Rape - the silent weapon".
The London-based group, which quoted a recent survey carried out by the CLEEN Foundation, a Nigerian non-governmental organisation, said that a total of 13,852 cases of rape and indecent assaults were reported between 1999 and 2005, with the highest figure of 2,284 cases recorded in 2001 alone.
Haz Iwendi, a Nigerian police spokesman, acknowledged that rape was a problem within the country's security forces, but said the government was already working to overcome it, citing a police workshop on sexual violence held in the capital on Tuesday.