Last year 28 boats were attacked in the western Indian Ocean but none taken captive in the region, the United Nations Institute for Training and Research (UNITAR) said in a report.
That compares to January 2011, when Somali pirates held 736 hostages and 32 boats, some onshore and others on their vessels.
"There has been a significant reduction in the number of pirate attacks during 2013, to the extent one can claim they have almost stopped," UNITAR said after its five-year study.
Much of that was down to the international fleet that has started to patrol the Gulf of Aden and Indian Ocean, and many merchant vessels have started keeping armed guards onboard.
Attacks have also become far less severe, with incidents involving rocket-propelled grenades falling from 43 in 2011 to just three last year.
At the same time the pirates' ransom haul fell from USD 150 million in 2011 to USD 60 million the following year.
Meanwhile in Southeast Asia piracy has surged, particularly in the maritime trading hub of the Malacca Straits, between Malaysia and Indonesia.
Attacks in the region topped 150 last year after starting an upward trend since 2010, said UNITAR.
"Piracy in the Malacca Strait continues to be a major disruptor for safe routes in the eastern Indian Ocean," said thew agency.
Last month the International Maritime Bureau said that there had been 23 actual or attempted attacks in Southeast Asian waters between January and March, mainly off Indonesia.
"With changing climatic conditions at high latitudes and medium-to-low-income countries in Asia experiencing the largest growth per capita, additional transport routes may be explored," it added.
Another focus of piracy is Africa's Gulf of Guinea off West Africa, where there were 50 pirate attacks last year.
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