Roh Moo-Hyun said the reclusive Kim was pleased with progress in six-party talks and at a perceived turn-around in Washington's attitude, according to Yonhap news agency.
"We have no intention to possess nuclear weapons. Our will is strong," Roh quoted Kim as saying at last week's three-day summit.
The comments came as US experts arrived in North Korea to plan the disabling of its plutonium-producing reactor and two other facilities at Yongbyon.
At six-party talks last week the North pledged to carry out the disablement, with the help of US experts, by year-end.
In return, the energy-starved communist state will get a total of one million tons of heavy fuel oil or equivalent economic aid plus major diplomatic and security benefits.
Washington has promised to work towards removing the North from its list of state sponsors of terrorism, and eventually normalising ties after full denuclearisation.
But some analysts believe that while he may shut down his plutonium-producing programmes, Kim will never surrender the atomic weapons his country spent decades developing.