The reclusive leader made the remark after South Korean President Roh Moo-hyun asked that South Korean companies operating at an industrial park in the North Korean city of Kaesong be allowed to use the Internet, Yonhap news agency reported, without citing any source.
"I'm an Internet expert too. It's all right to wire the industrial zone only, but there are many problems if other regions of the North are wired," Kim told Roh, according to Yonhap.
"If that problem is addressed, there is no reason not to open" the Internet, Kim said.
This week's summit - the second-ever such meeting between the two Koreas - produced a wide-ranging reconciliation pact that calls for establishing a new special economic zone in North Korea and expanding the Kaesong factory park.
North Korea is one of the world's most closed-off nations, with the totalitarian regime tightly controlling outside information and tolerating no dissent. Radios and TV sets in North Korea can only receive state broadcasts and ordinary people are banned from using mobile phones, let alone the Internet.
However, the country's ruling elite appear to have regular access to outside information.
Kim reportedly asked former U.S. Secretary of State Madeleine Albright for her e-mail address when she visited Pyongyang in 2000. A North Korean general cracked a joke about U.S. President George W. Bush during high-level military talks with the South earlier this year, saying he read it on the Internet.
The North's leader is also a big fan of South Korean movies and TV dramas, and Roh gave him a bookcase of South Korean DVDs as a gift this week.