Pirates holding Saudi tanker carrying two million barrels of oil set 10-day deadline.
The UN vote came as a group of Somali pirates demanded a ransom of $25m for the Saudi supertanker they hijacked last weekend, and warned of disastrous consequences if the sum was not paid within 10 days.
Pirates captured another three ships since the Sirius Star was taken, prompting an international naval force to patrol the waters around the Horn of Africa.
Somalia has lacked an effective government since the 1991 removal of Mohamed Siad Barre, the former military ruler, which sparked the ongoing conflict.
The Union of Islamic Courts movement (UIC) and its supporters control much of the south of the country.
Feuding, heavily-armed clan-based militias control many areas and a weak, Western-backed interim government has little authority outside the capital, Mogadishu.
The lawlessness has also spread onto the seas surrounding Somalia, with pirates carrying out an increasing number of attacks on ships that pass through the area.
Several envoys called for renewal of a June council resolution authorising states to enter Somali waters to combat pirates when it falls due next month, but many said the piracy problem stemmed from the general chaos on land.
“This piracy will never be settled until we address the situation in Somalia,” said Dumisani Kumalo, the South African envoy.
The council’s action comes as the African Union urged the UN on Thursday to quickly send peacekeepers to Somalia.
Ban Ki-moon, the UN secretary-general, has proposed that the current 3,450-strong African Union force there be replaced by an international stabilisation force with two multinational brigades, one of which could incorporate the AU troops.