The two leaders agreed at their summit to co-operate more closely in efforts to end North Korea's nuclear arms programme.
Lee's left-leaning predecessor, Roh Moo-Hyun, refused to visit Japan after December 2004 in anger over visits by Junichiro Koizumi, then Japan's prime minister, to the Yasukuni shrine that venerates Japanese war dead, including war criminals.
"Politicians make various comments, but there is no need to react sensitively each time", said Lee.
"It is a plus for the prosperity of both countries and for the peace and prosperity of North Asia for Japan and South Korea to walk together into the 21st century".
Lee also said he would welcome a visit by Emperor Akihito.
This would mark the first by a Japanese royal to the Korean peninsula since South Korea's independence.
North Korean challenge
Fukuda, an advocate of warmer ties with Japan's Asian neighbours, said that "North Korea is the greatest challenge for both Japan and South Korea".
Lee has pledged to take a tougher line against North Korea after ending a decade by liberal leaders in Seoul who stressed reconciliation with their neighbour.
"Politicians make various comments, but there is no need to react sensitively each time"
Lee Myung-bak, South Korea's President
Japan has tense relations with North Korea because of concerns over the North's nuclear programme and a dispute over Pyongyang's kidnappings of Japanese civilians in the 1970s and 1980s.
The two leaders also to open working-level talks aimed at restarting stalled negotiations on a free trade deal,
Tokyo and Seoul launched negotiations for a free trade deal in December 2003, but the talks stalled a year later because of bitter wrangling over tariffs.Lee said he was aware of concerns in South Korea that a trade pact may hurt its industries, but he said he talked with Fukuda about co-operation between Japanese and South Korean sectors and smaller companies.