African Union (AU) troops raped women and girls seeking medical aid or water from their bases in Somalia's capital, Mogadishu, a rights group says.
The troops had "misused" their power over women fleeing violence and poverty, Human Rights Watch (HRW) said.
One Muslim girl, aged 15, reportedly had her headscarf ripped off before being raped.
The AU, which has some 22,000 troops fighting militant Islamists in Somalia, says it will investigate the claims.
In 2012, the UN recorded 1,700 rapes in camps for displaced people in Somalia.
Many were thought to have been carried out by members of the Somali security forces.
'Raped girl paid'
Last year, there was a huge public outcry following claims that AU and government soldiers had gang-raped a woman in Mogadishu.
A joint investigation by the AU and government dismissed the allegation as unfounded, even though neither the woman nor independent witnesses had been interviewed.
Most of the women who were abused lived in camps for displaced people after fleeing violence and the 2011 famine, HRW said.
"The AU can no longer turn a blind eye to the abuses on Amisom [AU Mission in Somalia] bases, as it's undermining the very credibility of the mission," said Liesl Gerntholtz, HRW's women's rights director.
It interviewed 21 women and girls, some as young as 12, who described being raped or sexually exploited by Ugandan or Burundian soldiers in the AU force, HRW said.
Only one rape case, in which the victim was a child, is before Uganda's military court in Kampala, it added.
"Some Amisom soldiers have used humanitarian assistance, provided by the mission, to coerce vulnerable women and girls into sexual activity," HRW said.
"A number of the women and girls interviewed for this report said that they were initially approached for sex in return for money or raped while seeking medical assistance and water on the Amisom bases, particularly the Burundian contingent's base."
A Burundian soldier gave a 15-year-old girl $10 (£6) after raping her, HRW said.
"First he ripped off my hijab [headscarf] and then he attacked me," it quoted her as saying.
The girl had gone to an AU base of Burundian soldiers to collect medicine for her mother who was ill, HRW said.
Somalia has been hit by instability since the overthrow of long-serving ruler Siad Barre in 1991.
The AU force was deployed in 2007, with most of its troops coming from Uganda and Burundi.