The two nations this week began a joint survey to verify ownership
Kenyan MPs have expressed fury over remarks made by Uganda's president about ownership of the Migingo islands.
Ugandan President Yoweri Museveni said on Monday the islands belonged to Kenya but the water around the one-acre rock was Ugandan.
He suggested that no Kenyans should be allowed to fish off the Migingos under existing boundaries drawn up in 1926.
Parliamentarians in Nairobi want the African Union and the United Nations Security Council to resolve the row.
The two East African nations are conducting a joint survey to verify ownership of the Migingos in the rich fishing waters of Lake Victoria.
The exercise is due to last two months and both countries have agreed to call an independent expert in case of further dispute.
President Museveni triggered a fresh diplomatic row over the Migingos when he told the BBC on Monday: "The island is in Kenya, the water is in Uganda.
"But the [Luos, a Kenyan ethnic group] are mad, they want to fish here but this is Uganda."
On Wednesday, one MP in the Kenyan capital accused the Ugandan president of "exporting his dictatorial tendencies".
Another wondered if they should continue to regard Uganda as a friendly country.
Yet another said Kenyan President Mwai Kibaki must consult the UN as she said the Migingo dispute posed a threat to international peace and security.
Furious protesters in Nairobi reacted to Mr Museveni's remarks by uprooting railway lines linking Kenya and Uganda.
The BBC's Anne Mawathe says this caused disruption for landlocked Uganda, which relies heavily on Kenya to transport its goods.
In the Ugandan capital Kampala, the BBC's Joshua Mmali said Mr Museveni's spokesman found himself in the difficult position of having to deny his boss' remarks.
"His Excellency's statement has been misconstrued, misunderstood and taken out of context," he said.