"I am aware that people want to make sure that the abduction issue is not ignored ... the United States will not abandon you on this issue," Bush said.
High on their agenda was also the issue of North Korea's nuclear disarmament.
Bush said North Korea's nuclear declaration was a positive step but there was more to be done to ensure the safety of the Korean peninsula.
"We are concerned about enrinched uranium ... I view this process as a multi-step process, where there'll be action for action," he said.
Fukuda said Japan and the US would continue to work together closely, underlining the strength of their diplomatic and economic ties.
"The participants this year will discuss global issues, including the immediate dangers posed by the soaring prices of crude oil and foodstuffs"
Yasua Fukuda, Japan's prime minister
Canada, France, Germany, Italy, Russia and the United Kingdom, together with Japan and the US, make up the G8 membership.
Hundreds of anti-globalisation protesters were being kept up to 150km away from the summit venue on Sunday.
Activists held demonstrations for a second straight day in Sapporo, the closest major city to the summit area.
"Down with the G8 summit!" chanted some 100 demonstrators from left-wing labour unions, who were nearly outnumbered by riot police.
Al Jazeera's Stephen Cole, reporting from Japan, said the deployment of 21,000 police had turned the northern Japanese island of Hokkaido into a fortress.
"[The summit] is very important for Japan ... it's determined to show the world that it leads Asia, not China."
|What is the G8?
The G8 nations are the US, UK, Canada, France, Italy, Germany, Russia and Japan.
G8 concept first emerged in mid-1970s as informal forum for the world's leading industrialised democracies when it had just six members (the G6).
Canada joined the group in 1976 and the group became the G8 when Russia formally joined in 1997.
Group has rotating presidency responsible for planning and hosting annual meetings. This year Japan chairs the meetings.
In 2005 five outreach countries were added to the forum (the G8+5), representing five leading emerging economies: Brazil, China, India, Mexico and South Africa.
Topics to be discussed at the G8 meeting include the political turmoil in Zimbabwe and aid to Africa.
"The participants this year will discuss global issues, including the immediate dangers posed by the soaring prices of crude oil and foodstuffs as well as climate change," Fukuda said in a statement.
"They will also discuss international assistance to African development and the dual threats to world peace posed by the proliferation of weapons of mass destruction and terrorism."
The leaders of the G8 will be joined by leaders of 15 other countries, including China, India, Brazil, Australia and eight African states for expanded sessions on global warming and poverty alleviation.
Several officials have predicted that no significant progress will be made at the meeting, with Bush arguing that the summit is not the right forum to make hard decisions on climate change, including setting emissions targets.