The violence was triggered by the re-election of Goodluck Jonathan, a Christian from southern Nigeria.
Supporters of his main opponent, Muhammadu Buhari, a Muslim from the north, demonstrated against the outcome, saying that the election had been rigged.
The protests quickly turned violent, with Muslims attacking Christians they suspected of having supported Jonathan and the ruling People's Democratic Party.
Churches, homes and businesses of suspected supporters were set on fire and Christians were killed.
The Christian Association of Nigeria estimates that at least 170 Christians were killed in the riots.
Muslims and Christians interviewed by HRW estimate that more than 500 were killed in the predominantly Christian southern Kaduna State. Most of the victims in this region were Muslims.
HRW estimates that in northern Kaduna State, at least 180 people were killed in the cities of Kaduna and Zaria, in addition to dozens killed in other northern states.
"The April elections were heralded as among the fairest in Nigeria's history, but they also were among the bloodiest," said Corinne Dufka, senior West Africa researcher at Human Rights Watch.
"The newly elected authorities should quickly build on the democratic gains from the elections by bringing to justice those who orchestrated these horrific crimes and addressing the root causes of the violence."
The report was based on interviews conducted by HRW with 55 witnesses, including Christian and Muslim clergy, and police.
One lecturer described an attack on his college on the outskirts of Zaria: "When you see the mob, they were not in their senses.
"The students ran away but the mob pursued them into the staff quarters and they had nowhere to go. The mob beat them to death and hit them with machetes. Four Christian students and a Christian lecturer were killed."
HRW said it had received reports "excessive force" and "other serious abuses" committed by police and the military in their response to the violence.
It documented eight cases of police and soldiers killing unarmed citizens in Zaria and Kaduna, and said it had received reports of police and soldiers beating up detainees.
Dufka said: "The Nigerian authorities should promptly investigate these credible reports of unlawful killings and other abuses by members of the security forces.
"The use of violence by rioters, mobs, and state actors alike needs to be stopped."
A commission has been set up by President Jonathan to investigate the riots but there are some reservations about how effective it will be.
One Christian in the town of Kafanchan told HRW: "There have been commissions of inquiries set up in the past, but I don't know what they did. That is why we are really sceptical.
"I want to believe that if they had done justice, maybe a repeat of this wouldn't have come. This time justice should be done."