"We are seeking a delay before Lundin Petroleum starts to explore for oil," Ali Gorai head of the Pastoralists Community Development Organization (PCDO) told AFP.
"We need experts to come and find out why there are infections -- whether they were caused by other companies that explored for oil in our region in 1980s," he added.
Previous exploration in the 1980s left waste that local people suspect polluted wells, causing infections among the Turkana people.
"People (were) exposed to dangerous chemical. Cases, including cancer and respiratory disease, were not in our region there before oil exploration took place in the 1990s," said Gorai.
"What we are saying is that Lundin Petroleum should delay a start in their exploration until we are fully told why our people have been affected by the previous ventures that have nothing to do with company itself."
Gorai said the firm has been surveying the areas and was expected to start operations next month, despite the lack of an environmental impact assessment on the past the impact of previous explorations.
In October last year, Swedish firm Lundin Petroleum signed an agreement with the Kenyan government to explore oil deposits in the lake's Anza Basin for the next four years.
The basin, covering an area of some 14,748 square kilometers, is an extension of the Muglad Basin of Sudan, which has recoverable reserves of at least 300 million barrels of oil.
Kenyan geologists concluded the northwestern area was likely to have oil deposits after the discovery of oil and gas in neighbouring southern Sudan and along the Uganda-Democratic Republic of Congo border.
Lundin Petroleum scientists say oil exploration carried out in the 1980s in northeastern region yielded indicators of possible oil or gas deposits.