The Tamil Tigers, meanwhile, deny accusations that they are holding civilians as human shields.
He has criticised her for not even entertaining the idea of talking to the Tamil Tigers.
The separatist Tamil Tigers, or LTTE, are a proscribed terrorist organisation in many capitals.
But nor were the Tamil Tigers, under their leader Velupillai Prabhakaran, any more trusting.
The former head of the Sri Lankan military was widely credited with the 2009 victory over the Tamil Tigers.
In fact, Sri Lanka's Tamil Tigers rebel group was among the first in the world to deploy suicide bombers.
The biggest issue remains the long, drawn-out war against the separatist Tamil Tigers.
Jaffna, once the de facto capital of the Tamil Tigers, was captured by the government's men in May 1996.
Mr Wickremesinghe saw a surge in his Tamil support, after he had advocated foreign-aided talks with the Tamil Tigers.
Sri Lanka's army did the same after defeating the Tamil Tigers in 2009.
The conflict between government troops and the Tamil Tigers in the North-eastern region has also landed elephants in the cross-fire.
There is also an undercurrent of disappointment and sadness among many here that the Tamil Tigers had been wiped out.
Many ordinary Sri Lankans remain suspicious both of his liberal economic policies and of his policy towards the Tamil Tigers.
Although the Tamil Tigers are unquestionably on the back foot, it would be dangerous to discount them as a spent force.
The Tamil Tigers have been fighting in the north and east since 1983 and about 70, 000 people have been killed in the violence.
The island state has witnessed a violent insurgency for 25 years by the Tamil Tigers, a largely Hindu minority amid a mostly Buddhist Sinhalese majority.
He expressed great disappointment that his visit to Sri Lanka hadn't assisted the Tamil Tigers and the government there to broker a Northern Ireland-style deal.
Most of the fighting took place in the Tamil-dominated north, but the Tamil Tigers, or LTTE, also carried out suicide bombings in Colombo in the 1990s.
The allegations of child recruitment against Col Karuna are widespread - both from the time he was with the Tamil Tigers and after he left them.
Doctors there said she may have lost an eye during a suicide bomb attack - blamed on the Tamil Tigers during Sri Lanka's recent presidential election campaign.
Police in northern Sri Lanka have made a series of arrests which they say are linked to combating terrorism, three years after the separatist Tamil Tigers were defeated.
BBC: Sri Lanka arrests: Jaffna police detain 'terror' suspects
Of course, as Pape makes clear, extremist interpretations of Islam cannot be the sole factor behind suicide bombings, as the nominally Hindu group the Tamil Tigers aptly demonstrates.
But Western diplomats say a strong statement of concern has been sent from New York which will be closely followed by both the Tamil Tigers and Sri Lanka's government.
The Tamil Tigers and al Qaeda may not have religion in common, but they do share a dangerous worldview that justifies the killing of innocents, regardless of the circumstances.
The accusation is that these countries have outlawed the Tamil Tigers as terrorists but are now attending a meeting where they are represented as partners with the Sri Lankan Government.
In May 2009, Sri Lankan troops mounted a massive campaign to end the war against the Liberation Tigers of Tamil Eelam, a separatist group better known as the Tamil Tigers.
In the two years since Mr Rajapaksa's government started its military offensive, the Tamil Tigers have been beaten back steadily from vast swathes of territory they had dominated for years.
According to Bensman, since the mid-1990s, operative or affiliates of Hezbollah, Hamas, and the Tamil Tigers have been apprehended by U.S. authorities while jumping or after having jumped the border.
The attack was carried out by the Tamil Tigers, who for 14 years have been fighting for a separate homeland for the Tamil minority in the north-east of the island.
He says that his party has not ruled out a dialogue with the rebels, even though numerous UNP leaders have been assassinated by the Tamil Tigers over the last 17 years.
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