The two Burmese workers, whose names were given as Saw and Win, have been charged with the murder and rape of Hannah Witheridge, 23, and the killing of David Miller, 24, on the island of Koh Tao on 15 September.
They have already been paraded by police at a news conference, which also featured a re-enactment of the crime on the beach where the Britons’ bodies were found.
Amnesty said a lawyer acting for the accused had been told by one of the suspects that police had tortured him.
The UK-based charity cited the lawyer, from the Burmese embassy legal team, who said he had been told that police had beaten the suspect and “threatened him with electrocution”.
The Foreign and Commonwealth Office said it was concerned about the reports and expected a fair investigation.
Thai police, who have come under domestic political pressure to solve the case, deny the allegations and have said they have DNA and CCTV evidence to back up the confessions.
Amnesty added: “Numerous sources have also reported further acts of torture and other cruel, inhuman and degrading treatment of other migrant workers from Burma arrested by police in connection with the investigation. According to reports, police officers poured boiling water over some of the Burmese migrant workers they were questioning. Others were also beaten and threatened.”
Richard Bennett, Amnesty International’s Asia-Pacific programme director, said: “The Thai authorities must initiate an independent, effective and transparent investigation into mounting allegations of torture and other ill-treatment by police.
“The pressure to be seen to be solving an appalling crime that has garnered considerable attention should not result in the violation of rights, including to a fair trial.
“Authorities should provide protection from threats and acts of retaliation to anyone, regardless of their immigration status, reporting or speaking about torture or ill-treatment, and full redress to victims.
“They must also ensure that any alleged confession or information that has been coerced as a result of torture is not admitted as evidence in court, unless to prove that torture has been carried out.
“All suspects should also be guaranteed their rights to a fair trial – which is of particular importance in a crime that could carry a death sentence.”
A Foreign Office spokesman said: “We are concerned about the reports of allegations of mistreatment and expect these to be dealt with appropriately. The investigation and judicial process remains a matter for the Thai authorities, but we expect it to be conducted in a fair and transparent way.
“We remain in contact with them and have asked that they provide updates to the British embassy in Bangkok and the Foreign and Commonwealth Office in London.”
Previously, deputy police chief spokesman Colonel Kissana Phathanacharoen had said re-enactments of crimes were commonplace after confessions.
He said: “It’s carried out in order to get a sense of what happened after the confession. In Thai law the offenders have to give their consent. You can’t force them to do it.”