The December 20 concert in capital Colombo saw ecstatic local women running on stage to hug and kiss the "Hero" singer while others threw their underwear at him, Sirisena told a public meeting in the eastern district of Ampara.
"This is most uncivilised behaviour that goes against our culture," the president said.
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"I don't advocate that these uncivilised women who removed their brassieres should be beaten with toxic stingray tails, but those who organised such an event should be," he added.
Whipping with the tails of stingrays was reserved for hardened criminals in medieval Sri Lanka and is used as a popular idiom for extreme punishment of wrongdoing.
There was no immediate comment from the local organiser, Live Events, a company co-owned by Sri Lankan cricket stars Kumar Sangakkara and Mahela Jayawardene.
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In conservative Sri Lankan society, public displays of affection, even among married couples, is frowned upon. Police are known to have arrested courting couples for kissing in public parks or sea-front promenades.
Enrique fans had paid prices ranging from 5,000 rupees to 50,000 rupees ($350) to get to the live one-hour performance by the Latin pop star at a rugby stadium in Colombo which was part his world tour, "Love and Sex".
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