New York-based campaign group Human Rights Watch (HRW) says it has found evidence that three more prisoners have died in US detention in Afghanistan.
Donald Rumsfeld was told of claims of abuse and arbitrary detention
In an open letter to US Defence Secretary Donald Rumsfeld, it says the US is continuing to fail to investigate abuses or punish the guilty.
A US military official said the deaths were all under investigation.
Human Rights Watch also urged the US military to publish a delayed internal report on its Afghan detention centres.
The US authorities promised to release parts of the report several months ago and the BBC's Andrew North reports from Kabul that the Pentagon has not helped its image in Afghanistan with the confusion and delay that has surrounded it.
HRW says the three new cases of detainees dying in American custody bring to six the total it has documented over the past few years, four involving allegations of murder or manslaughter.
Lt Col Pamela Keeton, a spokeswoman for the US military in Afghanistan, told the Associated Press news agency that three of the cases were being investigated while three more were "in stages of adjudication".
Claims of torture
One of the new cases refers to a soldier from the US-trained Afghan army, who reportedly died after being wrongfully arrested in the Gardez area of eastern Afghanistan and repeatedly beaten by American troops.
Another allegation involves four US soldiers accused of murdering an Afghan detainee in 2002.
HRW says the case has only just come to light, because of the release of documents from an internal army investigation after a request by another US campaign group under the Freedom of Information Act.
The organisation - which has followed the actions of US forces in Afghanistan closely since they arrived in late 2001 - says it is aware of "only a handful of criminal investigations" into the cases and also many claims of torture by detainees.
It says it knows of only two US personnel being charged with any crime.
It said the US government's "failure to hold its personnel accountable for serious abuses has spawned a culture of impunity among some personnel".
Its letter to Mr Rumsfeld says there are fewer complaints now relating to the main US detention centre at Bagram airbase north of Kabul.
However, allegations of "abuse and arbitrary detention" continue to emerge from what are known as "forward operating bases" - smaller posts normally in frontline areas, it claims.
There is particular concern, it says, about the behaviour of special forces troops toward detainees at such bases.
The HRW letter also points out that the US-run detention system in Afghanistan operates entirely outside the rule of law.
Revelations of abuse
Although Red Cross officials are allowed to visit detention centres, their reports are never made public.
There has been criticism of procedures at detention centres
US commanders have repeatedly rejected requests for access from the Afghan Independent Human Rights Commission - the country's leading rights group, which also receives some US government funding.
The senior US commander in Afghanistan, Lt Gen David Barno, ordered the internal investigation in May, prompted by the revelations of abuse in Iraq.
US spokesmen promised that parts of the report - conducted by Brig Gen Charles Jacoby - would be released by the end of the summer at the latest.
HRW points out that similar investigations in Iraq have been released.
The US military in Afghanistan said on Monday that no date had been set for publishing the report because its findings were still being reviewed in Washington but Lt Col Keeton told AP that no abuses had been uncovered.
Gen Jacoby "found no evidence of abuse taking place... nor was there any evidence of leaders authorising or condoning abuse", the US military spokeswoman said.