"I recently read a piece of political humour on the internet called 'saving the president'," he was quoted as saying in pool reports from the talks.
Kim then went on to recount an often-told joke about the president out jogging when he a group of children save him from a sticky encounter with a speeding car.
(You can read the joke at the end of this page)
Kim's South Korean counterparts appeared unsure how to react to the unusual display of northern joviality.
In North Korea, where Kim Jong-il wields absolute power, former refugees have said attempts to demean the man referred to as "Dear Leader" mean certain punishment or even execution.
Previous North Korean references to the US president have tended to be highly politicised and vitriolic, variously referring to him as, amongst others, "a political idiot", "human trash", and "a tyrant that puts Hitler in the shade".
Border dispute
Train links between North and South have been
suspended for more than 50 years [Reuters]
Tuesday's talks were the first military-to-military contacts between the two sides in more than a year.
After the light-hearted start however, discussions became more serious when the North Korean side raised the contentious issue of its western sea border with South Korea.
Last year North Korea called off a planned rail test at the last minute after the South rebuffed its demand for redrawing the sea border.
North Korea does not recognise the current sea border, demarcated by the United Nations at the end of the 1950-53 Korean War, and has long claimed it should be further south.
The waters around the border are rich fishing grounds and boats from the two Koreas routinely jostle for position during the May-June crab-catching season.
In 1999 and 2002, their navy's skirmished, resulting in the deaths of several sailors and the sinking of six ships.
If the rail trial does go through, it will be the first train border-crossing in more than 50 years.
General Kim's joke

The South Koreans did their
best to look amused [Reuters]
Bush goes out jogging one morning and, preoccupied with international affairs, fails to notice that a car is heading straight at him.

A group of schoolchildren pull the president away just in time, saving his life, and a grateful Bush offers them anything they want in the world as a reward.

"We want a place reserved for us at Arlington Memorial Cemetery," say the children.

"Why is that?" asks Bush.

"Because our parents will kill us if they find out what we've done."