Six of the dead were children, and 30 people were wounded when the bombs fell on a Tamil fishing village, said the LTTE, which wants a separate homeland for minority Tamils in the north and east of the island.
The military has denied hitting civilians and said a well-identified Sea Tigers base had been bombed in the Mannar area after surveillance and radio intercepts.
"Sri Lankans continue to suffer deeply due to this conflict, and today's loss of life is a source of deepest concern," Margareta Wahlstrom, the UN assistant secretary-general for humanitarian affairs, said in a statement on Tuesday.
"It is imperative that both sides to the conflict take all measures to fulfil their obligations under international law to protect civilians in this conflict, we have too often seen them fall short."
The UN said more than 4,000 civilians displaced from the fighting last year were sheltered in the LTTE-controlled coastal village of Illupaikadavai in Mannar district where the bombing was carried out.
"The United Nations calls once more for a cessation of hostilities between the government of Sri Lanka and the Liberation Tigers of Tamil Eelam and resumption of the peace process"
Margareta Wahlstrom, UN assistant secretary-general for humanitarian affairs
"At least 14 civilians, including children, were killed this morning in north-western Sri Lanka during the aerial bombardment of the coastal village of Illupaikadavai in Mannar district by the Sri Lankan air force."
But the Sri Lankan air force said no civilian settlement in the Mannar area had been bombed and that the LTTE was spreading false information to discredit them and win international sympathy.
The LTTE has repeatedly accused the government of targeting Tamil civilians in areas under its control, but the government says the Tigers are using local people as human shields.
Fighting between the military and the Tamil Tigers has increased in recent weeks with the government vowing to dislodge the separatists from their eastern strongholds.
On Wednesday, the Tigers fired artillery and mortar bombs into an army camp in the Vakarai area, wounding four soldiers, the military said. Vakarai is one of the last big LTTE-controlled areas on the eastern coast.
More than 3,000 people were killed last year in suicide bombings, air and naval raids and clashes. Both sides say they stand by the 2002 ceasefire, but international monitors say it now exists only on paper.
"The United Nations calls once more for a cessation of hostilities between the government of Sri Lanka and the Liberation Tigers of Tamil Eelam and resumption of the peace process," the UN statement said.