The pirates had originally wanted £25m (£17m) to release the Sirius Star, which is carrying $100m (£67m) of oil and has 25 crew on board.
But Islamist spokesman Abdirahim Isse Adow, whose men are in the Harardhere area where the ship has been held offshore since its capture nine days ago, said the pirates had reduced their demands.
"Middlemen have given a $15m ransom figure for the Saudi ship. That is the issue now," he said.
The spokesman added that the pirates had moved the ship 62 miles off the coast of central Somalia because Islamist militia had been searching for them.
The revised ransom demand came as maritime groups urged the United Nations to take international action to halt the surge of piracy off Somalia.
Mr Adow, who represents the Islamic Court Union (ICU), said his men wanted to confront the pirates and release the Saudi Arabian Sirius Star because it was a "Muslim" ship.
"We are against this act and we shall hunt the ship wherever it sails and free it," he said.
The Islamists, who have been fighting the Somali government and its Ethiopian military allies for the last two years, condemn piracy in public.
But analysts say some of its members want a cut of the money and even use pirate gangs to enable weapons deliveries by sea.
Senior Somali government figures are also said to be keen to profit from piracy.
However, they deny seeking to profit from the crime, which has generated millions of dollars in ransoms this year.
The US navy, which is tracking the incident, has not confirmed or denied any ransom demand.
Author: Jo Amey
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Somali Pirates on $100m Oil Ship Reduce Ransom
Somali pirates holding a Saudi supertanker in the largest hijacking in maritime history have apparently reduced their ransom to $15m