Human rights activists have accused Kenya of secretly sending four terror suspects to Uganda after the World Cup bomb blasts in Ugandan capital Kampala.
Kenya's Muslim Human Rights Forum said this was a violation of Kenyan law.
The group's chairman, Al-Amin Kimathi, also said FBI agents interrogated three of the suspects illegally.
The US embassy said the US was aiding the investigation but did not comment on the role of the FBI. Nairobi has so far not commented on the affair.
The four suspects were arrested in different locations in Kenya following the twin bomb blasts that killed more than 70 people as large crowds watched the World Cup final on TV in Uganda's capital on 11 July.
Al-Shabab, a Somali Islamist group, said it carried out the attacks in revenge for Uganda's role in sending troops to Somalia as part of the African Union's mission to support the besieged government.
This week Uganda's chief prosecutor said 32 people had been charged in connection with the attacks.
Among the defendants are Ugandans, Kenyans, Somalis and a Pakistani.
Lawyer Mbugua Mureithi, who represents the Kenyan suspects' families, told the AP news agency that no attempts were made in Kenya to follow extradition procedures.
"Even more disturbing is that Uganda has not made a formal request to extradite the four nationals to Uganda," he said.
Three years ago, Kenya's government came in for criticism from human rights groups for rounding up and deporting to Somalia terror suspects accused of being members of an Islamist Somali militia.
They were flown to Ethiopia and allegedly questioned by US agents - then released a year later.
The case was referred to as "Africa's Guantanamo".