"Our alliance will endure and our efforts will be focused on revitalising that friendship so that it's even stronger and more successful in meeting the challenges of the 21st century," Obama said.
Hatoyama agreed, telling reporters: "I told him that the US-Japan alliance is the cornerstone of everything.
"But given the changing times and global environment, I would like to deepen the alliance and create a new US-Japan alliance that is constructive and future-oriented."
Al Jazeera's Rob Reynolds reports on the US president's first tour of Asia since taking office
Hatoyama has promised to halt a Japanese naval mission supporting the US-led war in Afghanistan, review basing agreements for 47,000 US troops stationed in Japan, and explore the possibility of a new Asian trading block that would exclude the US.
The US and Japan, the only country to have nuclear weapons used against it, also issued a joint statement saying that they would work together to "achieve total elimination" of the devices.
The two leaders also called on North Korea and Iran "to uphold and adhere to their respective international obligations".
Al Jazeera's Steve Chao, reporting from Tokyo, said that while much of the focus for Obama's visit has been on US-Japan security issues, the US president's main mission in Tokyo would be a wider-reaching one.
"He's trying to prevent what some are calling the 'Tokyo drift', which is a concern that Hatoyama and the newly elected government in Japan is moving towards a policy that is more independent of the US and away from the strategic alliance they have had for decades," he said.
In an interview with Japanese TV before the meeting, Obama acknowledged that Hatoyama's election had been a "political earthquake", but he downplayed talk of any resulting friction in relations between Japan and the US.
"This is not a senior-versus-junior partnership," he told Japan's NHK network.
"This is one of equals in which Japan has been an extraordinary contributor."
Robert Bianchi, a visiting professor at Qatar University's international affairs programme, said that the "tenor" of US-Japan relations had already been changing.
"Japan is being a bit more demanding with the United States and more accommodating with China. That is perfectly logical, I think they are bending with the wind and the US understands that and is not getting in the way," he told Al Jazeera.
"They [the new Japanese government] are still trying to sort out their foreign policy, but one thing that is clear is that everyone is relieved that they are presenting a kind of Japanese nationalism the rest of the world can live with, unlike their predecessors who were very solicitous to the right wing."
Air base tensions
The major focus of tension centres on the future of the Futenma US Marine air base on Japan's southern island of Okinawa.
|Local residents in Okinawa have objected to the continued US military presence [Reuters]
Under a 2006 deal the base is to be relocated to a less crowded part of the island.
Hatoyama, however, has said he wants the agreement to be reviewed and the base moved off the island, a suggestion the US has ruled that out saying it would undermine broader security arrangements that took more than a decade to negotiate.
Critics of the US presence in Japan have backed Hatoyama's suggestion, particularly residents of Okinawa which is home to more than half the US forces in Japan and a regular source of friction.
During his visit, Obama will also present what White House officials have called a "major policy speech" on US relations with Asia that they say will be aimed at a broad regional audience.
But no breakthroughs are expected on the issue of the military base.
Various street rallies were staged in Tokyo on Friday, including a small anti-US demonstration, but they passed off peacefully under the watchful eye of the some 16,000 police deployed to ensure security during Obama's visit.