They were joined by at least 10 armed men on Saturday, four days after the ship anchored off Harardheere with its 25 crew.
Somali fighters opposed to the country's interim government entered Haradheere on Friday in a bid to track down the pirates.
"We need immediate action from governments to protect these vital trade lanes - robust action in the form of greater naval and military support"
International Association of Independent Tanker Owners
Mohammed Adow, Al Jazeera's correspondent in neighbouring Kenya, said: "Mukhtar Robow, also known as Abu Mansour [a leader of al-Shabaab] confirmed to me that he has instucted his forces to storm Haradheere and Hoboyo, in central Somalia - both towns are pirate lairs.
"Robow said ... his forces will storm the ships that the pirates are controlling.
"He said he does not care if the ships are owned by Muslim countries or non-Muslim countries; his fighters will still storm them."
The world's largest oil tanker company has said a more aggressive military approach is needed to stop pirate attacks around the Horn of Africa.
"I think that is the only solution," Martin Jensen, the acting chief executive officer of Oslo-based Frontline Limited, said on Friday.
Some analysts have suggested that opposition fighters benefit from arms shipments and income gained through piracy.
The groups have denied the allegations and point to the decrease in maritime attacks during the Islamic Court Union's brief control of large parts of the country in 2006.
At least three other ships have been taken since the Sirius Star was captured and more than a dozen vessels with about 280 sailors on board are being held in Somali waters.
More than 120 attacks have been reported off the coast of Somalia this year.
More Somalis were becoming involved in piracy every day because of the money that can be made from the ransoms paid by ship owners.
The International Association of Independent Tanker Owners (Intertanko) has called for international action to tackle the situation.
"We need immediate action from governments to protect these vital trade lanes - robust action in the form of greater naval and military support with a clear mandate to engage, to arrest pirates and to bring them to trial," Intertanko said.
Many operators are considering sending their vessels around the tip of South Africa to avoid pirates, it said.
Efthimios Mitropoulos, the head of the International Maritime Organisation, spoke of "a series of negative repercussions" if ships had to reroute.
He said going around the Cape added about 12 days to a typical Gulf-to-Europe voyage, delaying oil supplies, and potentially raising freight rates by 25 to 30 per cent.
Mitropoulos said the UN Security Council should strengthen the mandate of anti-piracy forces with "clear rules of engagement" and force states to bring to justice any pirates they capture.
Nato sent four warships into the Gulf of Aden last month to prevent piracy and escort aid vessels, while a European Union anti-piracy operation off the coast of Somalia is set to begin on December 8.
Several other nations, including Russia and India, also have navy vessels working to protect shipping in the area.
The Security Council on Thursday voted unanimously to impose sanctions on pirates, arms smugglers and other people involved in fuelling the instability in Somalia, which has been without a functioning central government since 1991.