Canada, France, Germany, Italy, Russia and the United Kingdom, together with Japan and the US make up the G8 membership.
Thousands of anti-globalisation protesters were being kept 70km away from the summit venue.
Al Jazeera's Stephen Cole, reporting from Japan, said the deployment of 21,000 police had turned the Japanese island of Hokkaido into a fortress.
"That [the summit] is very important for Japan ... it's determined to show the world that it leads Asia, not China."
On his trip, Bush hopes to drive home the message that Tokyo remains Washington's indispensable ally in east Asia despite increased ties with China.
"The cornerstone of US policy is good, strong relations with Japan"
George Bush, US president
"The cornerstone of US policy is good, strong relations with Japan," he said earlier in the week. "That's not to say we can't have good relations with China."
Bush also wants to rally support for pressuring North Korea to fully account for its nuclear weapons activities and finish dismantling its programme.
"We're at a very pivotal point in the six-party process and the president and the prime minister of Japan will want to compare notes and make sure we are working on the same page," Dennis Wilder, senior Asia aide on the US National Security Council, said.
Wilder said talks on how best to verify the accuracy of North Korea's June 26 "declaration" of nuclear activities could be held in Beijing as early as July 11 or 12.
Bush is to hold one-on-one talks with the leaders of Russia, China, Germany, India and South Korea later in the week.
Topics to be discussed include Iran's nuclear programme, the political turmoil in Zimbabwe and aid to Africa.
Tehran's rejection of a US-backed plan to halt uranium enrichment in exchange for fuel for a civilian nuclear effort from Moscow, is also on the agenda.
Dana Perino, the White House spokeswoman, said: "We're going out to consult with our allies about what Iran's response means."
Bush, who will celebrate his 62nd birthday in Japan on Sunday, also hoped that the G8 would yield a stiff condemnation of Robert Mugabe, Zimbabwe's president, as Washington pushes ahead with proposed UN sanctions against his government.
He also plans to press G8 countries to make good on past pledges to help Africa battle HIV/Aids and other deadly diseases, and help the continent grapple with the world food crisis.
Bush will also make the case that no global climate change pact can work unless "greenhouse gas"-producing developing nations like China and India accept some form of long-term goals for curbing emissions.