Earlier, Kim had proposed that his summit with South Korean President Roh Moo-hyun continue beyond its scheduled Thursday end. But a pool report from South Korean reporters, which did not cite any source, said the meeting would end Thursday and that the two leaders would announce an agreement that morning.
The summit is only the second time in the history of the divided Koreas that top leaders have met.
Kim appeared to warm to his South Korean visitor Wednesday after an initial chilly reception. CBS News reporter Don Kirk says Kim smiled pleasantly as he shook Roh's hand Wednesday - a noticable difference from the straight-faced greeting extended a day earlier.
According to South Korean pool reports, Roh told Kim he was concerned about flooding in the North, where this year's seasonal summer rains left some 600 people dead or missing and tens of thousands homeless. North Korea delayed the summit from its original late August date due to the disaster.
Before talks began at a state guesthouse in Pyongyang, Roh presented gifts to the North Korean leader that included a bookcase full of South Korean DVDs, featuring popular soap operas and films starring Lee Young-ae, believed to be Kim's favorite starlet. Kim is a known cinema buff who has a vast film library and purportedly has helped produce several movies.
The two men posed seated for a photograph along with other delegation members before starting their meeting. Kim was accompanied at the talks only by his spy chief, while Roh was joined by four top officials.
The morning session ended after just over two hours and the leaders were to resume meeting Wednesday afternoon, presidential spokesman Cheon Ho-seon told pool reporters in Pyongyang.
This week's summit is only the second time leaders of the North and South have met since the Korean peninsula was divided after World War II.
Wednesday was expected to be dominated by the leaders' talks, for which no specific agenda was publicly known, before Roh was scheduled to view an evening performance of the North Korean propaganda spectacle known as the "mass games." It was not known if Kim would also attend.
The show features thousands of synchronized gymnasts performing in front of a mural formed along the entire wall of a stadium by children turning colored pages of books.
Conservatives have criticized Roh for going to the show, which extols the purported virtues of the North's communist regime. The North has excised potentially embarrassing sections for the summit, and South Korean officials have noted other visitors have viewed the event - including then-U.S. Secretary of State Madeleine Albright in 2000.
During the opening day of the summit Tuesday, the North and South Korean leaders had no contact besides a 12-minute welcoming ceremony where they barely exchanged words. His demeanor appeared a stark contrast with the friendliness he offered Roh's predecessor, Kim Dae-jung, at the first-ever summit in 2000.
Instead, Kim let his deputy, the country's nominal head of state Kim Yong Nam, deal with the South Koreans at ceremonial meetings, where pool reports gave no details of any substantive issues being discussed. The North also hosted a banquet where Roh offered a toast to Kim Jong Il's health.
Roh has said he wants to use this week's summit to start a genuine peace process with North Korea instead of the current reconciliation track, which has seen halting progress in reducing military tension on the Cold War's last frontier.
The two Koreas remain technically at war since a 1953 cease-fire ended the Korean War, despite seven years of warming ties.
Roh has not given any specifics about what he will propose or seek, prompting criticism from conservatives at home that the summit is an ego trip for the South Korean leader to establish a legacy for his unpopular administration, which ends in February.
Both Roh and Kim also hope to keep the surging conservatives from winning South Korea's December presidential election. They hold a commanding lead in opinion polls. The main opposition Grand National Party is more skeptical of relations with the North, insisting aid be conditional on nuclear disarmament and reforms in the country's centralized economy.