KABUL—Opium cultivation in Afghanistan reached a record this year, a new United Nations survey shows, a major setback to over a decade of international efforts to combat the drug trade and persuade farmers to switch to legal crops.

The amount of land under opium cultivation jumped 36% to 209,000 hectares (516,000 acres) in 2013, according to the U.N. Office on Drugs and Crime and the Afghan counternarcotics ministry. "This is...