The newspaper on Saturday cited army criminal investigative reports obtained by Human Rights Watch that have not been made public.
They follow revelations of abuse of prisoners by US forces in Iraq and allegations of torture at the US base at Guantanamo Bay, Cuba, that have drawn widespread international criticism.
One soldier, Private First Class Willie Brand, was charged with manslaughter in a closed hearing last month in Texas in connection with one of the deaths in Afghanistan, another army document showed.
Brand, who acknowledged striking a detainee named Dilawar 37 times, was accused of killing him after maiming him over a five-day period by "destroying his leg muscle tissue with repeated unlawful knee strikes", according to the Times.
The reports provide the first official account of events that led to the death of Dilawar and another detainee, Mullah Habibullah, at the Bagram Control Point near Kabul.
The deaths happened nearly a year before the abuses at Abu Ghraib prison in Iraq.
The reports, from the Army Criminal Investigation Command, also make clear that the abuse at Bagram went far beyond the two killings, the newspaper said.
Among those recommended for prosecution is an army military interrogator who is said to have "placed his penis along the face" of one Afghan detainee and later to have "simulated anally sodomising him".
The army reports cited "credible information" that four military interrogators assaulted Dilawar and another Afghan prisoner with "kicks to the groin and leg, shoving or slamming him into walls/table, forcing the detainee to maintain painful, contorted body positions during interview and forcing water into his mouth until he could not breathe".
The treatment of prisoners at the
US base in Cuba has been criticised
US military officials in Afghanistan initially said the deaths of Habibullah, in an isolation cell on 4 December 2002, and Dilawar, in another such cell six days later, were from natural causes.
But after an investigation, the army acknowledged the deaths were murders, The New York Times said.