The report is an account of atrocities carried out during heavy fighting in the capital earlier on in the year, in which hundreds died and thousands were wounded.
The fighting, described as the heaviest ever in Somalia, created the worst displacement in Africa with more than 400,000 people fleeing Mogadishu in two months.
The New York-based rights group said most of the abuses were deliberate.
It also appealed to the international community for help, while denouncing "key players with strategic involvement in the region", such as the United States and the European Union, for inaction.
In one of Monday's attacks, police said four officers were killed in a landmine attack.
"A remote controlled landmine exploded near one of our vehicles carrying policemen. Four police officers died from the blast. This is definitely caused by the insurgents," Abdullahi Hassan Barise, a police commander, said.
Three other policemen were wounded, he said, adding that there could have been civilian casualties as the explosion had occurred in a busy area.
In another incident in south Mogadishu, one person died and three were wounded when a landmine targeting a police vehicle exploded and hit a bus instead, witnesses said.
"The police escaped unhurt. We were very fortunate we were not caught in the blast," Sheikh Salab, a local resident, said.
The attacks come soon after the killings of two prominent Somali journalists over the weekend and intensified assaults on Ethiopian-backed Somali troops by suspected fighters.