The Iraqi authorities denied the claims, which come with Baghdad locked in a months-long standoff with anti-government fighters in Fallujah amid a protracted surge in nationwide bloodshed, all of which is fuelling fears the country is slipping back into the all-out conflict of 2006 and 2007.
The New York-based rights watchdog also said abuses committed by the powerful Islamic State of Iraq and the Levant jihadist group -- among the main militant organisations in Fallujah -- likely amounted to crimes against humanity.
"In terms of what ISIL has taken responsibility for ... (they) have committed horrible crimes," said HRW's Iraq Researcher Erin Evers, pointing to the group's claims of having carried out suicide and car bomb attacks and summary executions.
"But to equate them with the crimes of a government that has rescinded responsibility for protecting its civilian population and ... Rescinded responsibility for respecting its own laws and international law, there is no way the two can be equated."
Militants subsequently seized parts of the provincial capital Ramadi and all of Fallujah, the first time anti-government forces have exercised such open control in major cities since the peak of the deadly violence that followed the US-led invasion of 2003.
They have held all of Fallujah since, and protracted battles have continued over Ramadi.