Amnesty International and Human Rights Watch, in a joint appeal, reminded Sudanese authorities that torture and other forms of abusive treatment were prohibited under international law.
The groups expressed concern about the treatment of the estimated 2,000 demonstrators rounded up by the government since protests erupted last month. They said that as recently as July 6, security forces had used force against demonstrators in Khartoum.
"We call on the Sudanese authorities to ensure that every credible allegation of such abuse is subject to prompt and impartial investigations, and to ensure that the victims receive reparations," said Aster van Kregten, Amnesty International's deputy director for Africa, in a statement from Kenya.
Sudan's economy was hurt by South Sudan's independence last year. Sudan, as part of the deal, maintained authority over export routes while South Sudan took control over most of the regional oil fields. South Sudan in January halted oil production to protest Khartoum.
U.S. officials had expressed concern about Khartoum's response to the demonstrations, saying the use of force was no way to address national economic concerns.