Rights groups are also calling for an independent investigation
Saudi authorities have ordered post-mortems on the bodies of two nationals repatriated from the US prison camp in Guantanamo Bay, Cuba.
At the same time,the family of a Yemeni prisoner said to have committed suicide at the prison is refusing to bury him, demanding an investigation into his death.
Nahez Ghazi al-Otaibi, cousin of dead Saudi detainee Maniy bin Shaman al-Otaibi, said on Saturday that "with our agreement, the authorities ordered post-mortems on the two bodies to establish the real cause of death before they are handed back to us".
The families of both Otaibi and the other dead Saudi, Yasser Talal al-Zahrani, were able to see their bodies shortly after their repatriation by the US authorities, the cousin added.
He renewed the families' accusations that the US account that the pair hanged themselves in their cells along with Yemeni detainee Ali Abdullah Ahmed was a cover-up.
"My cousin … was a good Muslim," Otaibi said in allusion to the religion's prohibition on taking's one's own life.
"He was one of the most tortured of Guantanamo detainees … because he refused to co-operate with his US interrogators," he added, citing the testimony of former Guantanamo detainees held with him.
"That's why he was banned from writing to his family who received just a single letter from him by mail."
In Yemen, the family of Ali Abdullah Ahmed is refusing to bury him, demanding an investigation into his death, the family lawyer said on Saturday.
"The family … is refusing to bury him and are asking for an autopsy to know the real reason behind his death"
Khaled al-Ansi, also a human rights activist, said "the family … is refusing to bury him and are asking for an autopsy to know the real reason behind his death".
Ansi said Yemen's public prosecutor has approved a request by Ahmed's family to investigate the death.
Last Thursday, Yemen said it had asked the US to probe the incident and expressed concern over the fate of other inmates still held at the facility.
US officials aroused worldwide outrage by describing the three suicides, the first in Guantanamo since the detention camp's opening in 2002, as "an act of asymmetric warfare" and "a good PR move".
The Pentagon on Tuesday rebuffed calls for an outside investigation into the June 10 suicides, saying the US military could review the situation itself.
But human-rights watchdog Amnesty International called for an independent investigation as "a matter of absolute urgency".