The South Korean minister overseeing inter-Korean affairs on Tuesday offered condolences to the Democratic People's Republic of Korea (DPRK) over its leader Kim Jong Il's death, announced a day ago by the DPRK's state media.

"(South Korea) extends sympathy to the people of North Korea ( DPRK)," unification minister Yu Woo-ik said in a statement following a meeting presided over by President Lee Myung-bak.

"We hope North Korea would restore stability soon so the South and the North can cooperate on achieving peace and prosperity on the Korean Peninsula," Yu said.

Yu added the government has decided not to send an official delegation to attend Kim Jong Il's funeral as the DPRK said it would not accept foreign delegations for the funeral ceremony scheduled on Dec. 28.

Still, the government will allow Pyongyang visits by the families of late former South Korean President Kim Dae-jung and former Hyundai Group chairman Chung Mong-hun, in appreciation of Pyongyang's previous decisions to send delegates to honor the two men at their funerals, Yu said.

Former first lady Lee Hee-ho, whose late husband had forged friendly ties with the DPRK that culminated in a historic joint summit in 2000, has voiced hope for a Pyongyang visit even before Kim's death.

Hyundai Group chairwoman Hyun Jung-eun, who remains committed to the troubled cross-border tourism business since her husband Chung Mong-hun killed himself in 2003, offered condolences over Kim's death in a press release Monday.

The DPRK announced a 13-day mourning period through Dec. 29.