Barack Obama, who is on a four-nation Asia tour, warned against escalation in the dispute and said he wanted to see the row resolved peacefully.
He confirmed that the islands fell under a security treaty that commits the US to act if Japan is attacked.
Barack Obama and Shinzo Abe also discussed a major trade deal as well as North Korea.
The US president arrived in Japan late on Wednesday ahead of stops in South Korea, Malaysia and the Philippines.
He is not going to Beijing but relations with China are expected to dominate his meetings with regional leaders.
Barack Obama’s trip – which ends on April 29 – comes nearly seven months after he cancelled a visit to the region because of a US government shutdown.
Officials say it is aimed at reassuring America’s Asian allies of its commitment to the region amid concern over China’s growing power.
On Wednesday Barack Obama had an informal dinner with Shinzo Abe. The two leaders then held talks on Thursday morning and gave a joint press conference.
“Article five [of the US-Japan security treaty] covers all territories under Japan’s administration including [the] Senkaku islands,” Barack Obama said, echoing comments published in Wednesday’s Yomiuri newspaper.
“We do not believe that they should be subject to change unilaterally.”
“This is not a new position. This is a consistent one,” he said.
However, Barack Obama also said he told Shinzo Abe that it “would be a profound mistake to continue to see escalation around this issue instead of dialogue”.
The islands are called Senkaku in Japan and Diaoyu in China.
Japan controls the islands but China has been strongly pressing its claim in recent months, flying and sailing vessels in and out of what Japan says are its waters and airspace.
Japan depends on the US for its security, under a decades-old alliance that dates back to the end of World War Two. If Japan is attacked, the US is obliged to come to its aid.
China’s foreign ministry said on Wednesday that it opposed the US stance.
“The so-called US-Japan alliance is a bilateral arrangement from the Cold War and ought not to harm China’s territorial sovereignty and reasonable rights,” spokesman Qin Gang said in Beijing.
Shinzo Abe and Barack Obama also discussed the Trans-Pacific Partnership, a giant trade deal involving 12 nations.
It is currently stalled partly due to a row between the US and Japan over agricultural tariffs.
North Korea was also on the agenda. Barack Obama wants Tokyo and Seoul to work together on the issue, but ties between the two remain badly strained because of war-related historical issues.
Barack Obama flies to Seoul after Tokyo, amid reports of increased activity at Pyongyang’s nuclear test site – potentially suggesting a fourth nuclear test could be imminent.
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