The sister of North Korean leader Kim Jong Un has warned of retaliatory measures against South Korea that could involve the military, in the latest escalation of tensions over defectors from the North who have been sending back leaflets and food.

Kim Yo Jong, who serves unofficially as one of Kim Jong Un's top aides, issued the warning in a statement carried by the state-run Korean Central News Agency on Saturday.

"By exercising my power authorized by the Supreme Leader, our Party and the state, I gave an instruction to the ... department in charge of the affairs with (the) enemy to decisively carry out the next action," she said.