The Tanzania Albino Society (TAS) has called for the men found guilty of killing an albino boy to be hanged publicly as a warning to others.
A court sentenced them to death for attacking the boy and severing his legs for use in witchdoctors' potions.
The BBC's John Ngahyoma in Dar es Salaam says there are more than 100 people on death row, but no-one has been executed in more than 15 years. But TAS chairman Ernest Kimaya urged the president to endorse the sentence.
"I want other perpetrators to learn - seeing is believing," he told the BBC.
Mr Kimaya told Tanzania's Citizen newspaper that a public execution would also "show that the government is serious in its war on albino killers".
In the past two years, 53 albino people have been murdered in Tanzania. For example, one teacher in the northern town of Arusha has been arrested for killing his own child, who was albino. As well as the four killings, the body of an albino has also been exhumed. It was found with its limbs cut off.
Albino people, who lack pigment in their skin and appear pale, are killed because potions made from their body parts are believed to bring good luck and wealth. Renegade witch doctors have convinced locals that there are magical properties in the blood, bones and skin of people with albinism, which has created a sickening black market where the limb of an albino can bring in anywhere from $500 to $2,000. In a country where the per capita income is roughly $450 a year, that's a macabre fortune.
The Tanzanian government has publicly stated its desire to end the killings. In March, President Jakaya Kikwete called on Tanzanians to come forward with any information they might have.
Officials banned witchdoctors from practicing, however many have continued to work. Many of Tanzania's estimated 17,000 albino people are now living in fear, especially in villages in the north-west where the majority of the murders have occurred. The case in Kahama on Wednesday was the first conviction in Tanzania for an albino killing.
Correspondents say there is also a fear of reprisal killings as witchdoctors and their clients wield a lot of power in their communities. Witchdoctors in Tanzania and other parts of East Africa have made tens of thousands of dollars from selling potions and other items made from the bones, hair, skin and genitals of dead albino people. They pay a lot of money for body parts.
In July a court in neighboring Burundi sentenced one person to life in prison and eight others to jail for the murder of albino people whose remains were sold in Tanzania.
In the early 2000s similar incidents of trading in human organs were reported to have surfaced in the country. At that time six people were believed to have been killed and skinned in Mbeya Region, south-west of Tanzania.
There was, according to media reports, a high demand for human skin in Malawi, Zambia, Mozambique, South Africa and the Democratic Republic of Congo and one human skin would sell at between Sh168,000 (approximately US$134.4) and Sh672,000 (approximately US$537.6) at the time.
Ever since independence in 1960, Tanzania has been known as a haven of peace and political stability. Yet, this fame is slowly fading away as rampant corruption, mismanagement of national resources, poverty, the cost of living and despicable crimes are also increasing.
Although superstitious beliefs may fall under the category of complex phenomena in the society, they are, however, about control and survival mechanisms. The more powerful one is the more influential and successful one is believed to become socially, economically and politically.
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