Iraq declared victory over the Islamic State group in Mosul earlier this week after a nearly nine-month battle that ravaged the city and took a heavy toll on residents and security forces.
The videos "appear to show Iraqi soldiers and federal police beating and extrajudicially killing detainees", the rights group said in a statement that included links to the clips, which were posted on Facebook.
In one video, men in Iraqi army uniforms beat a bearded detainee, drag him to the edge of a cliff, throw him off and shoot him and another body at the bottom.
Those videos, which show men in army and police uniforms beating detainees, were still viewable on Facebook, where they were posted by a man HRW said "regularly publishes information regarding security and military activities in and around Mosul".
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"In the final weeks of the battle for west Mosul, I observed first-hand the desire of armed forces to get the battle wrapped up as quickly as possible," HRW's senior Iraq researcher Belkis Wille said.
An Iraqi journalist embedded with the Rapid Response Division earlier in the operation reported that members of the special forces unit carried out torture, rapes and killings.
The journalist, who has since left Iraq, documented some of the abuses on film.
IS overran Mosul and swathes of other territory in the summer of 2014, but Iraqi forces backed by US-led air strikes have since regained much of the territory they lost.
Abuses by security forces now are likewise a boon to IS, which is likely to increasingly revert to bombings and hit- and-run attacks as its cross-border statehood project continues to fall apart.