LONDON — Urging the destruction of an “entire category” of unconventional weapons, the Norwegian Nobel Committee awarded its 2013 Peace Prize on Friday to a modest and little-known United Nations-backed organization that has drawn sudden attention with a mission to ensure that Syria’s stocks of chemical arms are eradicated.

The award, to the Organization for the Prohibition of Chemical Weapons, surprised some Nobel watchers partly because of the unprecedented nature of its current task: overseeing the destruction of a previously secret chemical weapons program quickly amid a raging civil war.

“We were aware that our work silently but surely was contributing to peace in the world,” Ahmet Uzumcu, the director general of the organization, told reporters at its headquarters in The Hague after the award was announced. “The last few weeks have brought this to the fore. The entire international community has been made aware of our work.”