CNN) - North Korea will admit delegations from the South that wish to visit Pyongyang to express their condolences following the death of the leader Kim Jong Il, according to a statement posted on a government website run by the North.

"We will guarantee all convenience and safety of the South Koreans during their visit," said the statement on uriminzokkiri.com, dated Thursday, adding that the North would open to the delegations "all air routes and land routes through Kaesong," its industrial park, some 45 kilometers (27 miles) north of Seoul.

After Pyongyang announced on Monday the death of Kim, the dictator who had ruled the secretive dictatorship since 1994, Seoul has made a number of gestures as it tries to navigate the uncertainty created by the North's leadership transition. Pyongyang has named Kim's youngest son, Kim Jong Un, as the "Great Successor" to his father.

Seoul expressed its sympathy to the North Korean people through a statement on Tuesday. South Korea also said that while it would not send an official delegation to the North, it would allow a limited number of private groups to send delegations to the North if desired.