The victims, according to their legal representative, are looking to get remedies for bodily harm they have suffered, and compensation.
Several Rwandans who say they were illegally arrested and tortured by Ugandan security agencies are filing a lawsuit at the East African Court of Justice.
Kigali-based lawyer Richard Mugisha, of Trust Law Chambers, is representing the victims - who include a couple that welcomed their first born in a Ugandan detention facility, and another man.
Each of the complainants spent at least nine months in custody.
They were deported in last April, Mugisha said.
"We are preparing their case before filing a lawsuit," he said.
"There are laws that govern EAC member states," he added, in reference to the East African Community, a six-nation regional bloc to which both Rwanda and Uganda subscribe.
The victims, their legal representative said Monday, "are looking to get remedies for bodily harm they have suffered, and compensation."
The couple, Ezechiel Muhawenimana, 36, and wife Esperance Dusabimana, 35, who were detained for nine months are seeking US$100,000 while the third person, Venant Musoni Hakolimana, a teacher, is demanding US$1 million from Ugandan authorities.
"They want compensation because they were dispossessed of their money and subjected to forced labour, among other things," said Mugisha, who told reporters in Kigali that he was representing the victims on pro-bono basis.
City lawyer Richard Mugisha (in the background) speaks to journalists shortly before filing the case at the East African Court of Justice office in Kimihurura.
The couple are farmers from Rubavu District while Hakolimana hails from Ngororero District.
Five other torture victims recently deported from Uganda have also contacted the lawyer, he said.
"We trust the court will give the victims justice expeditiously," Mugisha said.
The couple were arrested on July 23, 2018 as they went to attend a funeral for a family member in Mubende, central Uganda. They say they were removed from a bus in an area known as Rubanda in Kabale, south-western Uganda.
Security agents who arrested the couple took Rwf80,000 from them, they say.
As for Hakolimana, he says he was detained in a Ugandan military intelligence 'safe house' on July 12, 2018 before he was released on April 24, 2019.
He says he had to go to the Rwandan High Commission in Kampala to ask for assistance to return to Rwanda.
He says he was arrested on his way to his home in Mbarara, western Uganda.
"I was charged with illegal entry into Uganda which was not true because they confiscated my travel documents," he said. "I was also accused of being involved in espionage on behalf of Rwanda Defence Force, which is not true."
After spending months in a non-gazetted detention facility run by Uganda's Chieftaincy of Military Intelligence (CMI), he was produced before a judge who ordered him to pay a fine of 1 million Ugandan Shilling (about Rwf250, 000) and then released.
"I was illegally jailed for nine months in a CMI dungeon," he said.
The three claimants are among dozens of Rwandan citizens who were arbitrarily arrested and later released by Ugandan security agencies in a systematic crackdown on Rwandan nationals in Uganda - a situation that has severely strained relations between the two countries.
Kampala claims those it arrests are law-breakers who are spying on the Ugandan government, while Kigali insists the arrests and subsequent torture of Rwandans are part of a broader hostile scheme by Kampala that includes facilitating and funding dissidents bent on destabilising Rwanda.
Kigali says President Yoweri Museveni's government is hosting and facilitating agents of a myriad of armed groups that seek to destabilise Rwanda.
Increased disappearances of Rwandan nationals in Uganda forced the Government to issue a travel advisory back in March, which still stands.
Last week, Uganda deported as many as 20 Rwandans at once, most of them, ADEPR Pentecostal church evangelists, the largest single group to be deported in the wake of the standoff.
Most deportees have told tales of inhumane treatment and torture at the hands of Uganda's security forces, especially intelligence agents and operatives linked to Rwandan terror group RNC.
Most of them were never charged in court and Rwanda says Uganda still holds scores of innocent Rwandans, who it says have been deprived of their right to consular and legal services.
RNC was created by Rwandan fugitives, including former senior military officers wanted in Rwanda over terrorism-related cases for which they were tried in absentia and sentenced to varied jail terms.
The group is linked to a spate of fatal grenade attacks that rocked the capital Kigali about 10 years ago.
Uganda has also been linked to other anti-Kigali armed groups, including FDLR, the offshoot of forces and militia largely blamed for the 1994 Genocide against the Tutsi, and FLN, which last year made incursions on Rwandan territory through Burundi, killing at least nine civilians and wounding several others.
Details of Uganda's support to Rwandan rebel groups has partly been revealed by senior FDLR and FLN leaders who were arrested within the last six months and are appearing before courts of law.
A UN report of experts released in December also said Uganda was a major source of new recruits for 'P5', a coalition that brings together different Rwandan rebel groups led by RNC's Kayumba Nyamwasa. Nyamwasa is based in South Africa.
President Museveni admitted in a letter to his Rwandan counterpart Paul Kagame in March to "accidentally" meeting in his office RNC officials, but denied Kampala was offering support to anti-Kigali armed groups.