TOKYO — Showing solidarity with Japan, President Barack Obama yesterday in Japan affirmed that the U.S. would be obligated to defend Tokyo in a confrontation with Beijing over a set of disputed islands, but urged all sides to resolve the long-running dispute peacefully.Wading cautiously into a diplomatic minefield, Obama insisted the U.S. takes no position on whether the islands in the East China Sea are ultimately in the dominion of China or Japan. But he noted that historically Japan has administered the islands, triggering America's treaty obligations to defend its ally should tensions escalate militarily. "We do not believe that they should be subject to change unilaterally," Obama said at a news conference with Japan's Prime Minister Shinzo Abe. "What is a consistent part of the alliance is that the treaty covers all territories administered by Japan."The dispute over the islands, called Senkaku by Japan and Diaoyu by China, has badly strained relations between the two Asian powers. Although Obama has sought to avoid getting dragged in to territorial disputes an ocean away, Japan and other U.S. allies see the disputes through the broader lens of China's growing influence in Asia, where Obama arrived Wednesday at the start of a four-nation, eight-day tour.China is not on Obama's itinerary, but concerns about the Asian powerhouse are trailing the president nonetheless. Beijing is watching closely for signs that U.S. is seeking to limit China's rise, while smaller nations are looking to Obama for affirmations that his vaunted push to increase U.S. influence in Asia hasn't petered out. "We want to continue to encourage the peaceful rise of China," Obama said.Seeking to inject fresh urgency into trade talks, Obama said the time is now to resolve issues hindering completion of the Trans-Pacific Partnership. The U.S. has been leading the 12-nation negotiations, but an end-of-2013 deadline was missed and there are few signs of progress toward resolving conflicts with Japan over tariffs and access to Japan's auto market. "Abe's got to deal with his politics, I've got to deal with mine," Obama said. On the island dispute, Obama encouraged the parties to work through the issue "through dialogue" and urged both sides to "keep the rhetoric low." He downplayed the U.S. commitment to defend Japan as a matter of historical fact rather than a rebuke to China. "The treaty between the U.S. and Japan preceded my birth, so obviously this isn't the red line that I'm drawing," the president said.Abe said he and Obama agreed to cooperate on engagement with China and other issues, including Okinawa, where the U.S. military presence remains a source of tensions. "The Japan-U.S. alliance is more robust than ever before," Abe said through a translator.Addressing another source of tension in the region, Obama said he's not optimistic North Korea will change its behavior in the near future. But he said he's confident that by working with Japan, South Korea and others especially China the U.S. can apply more pressure so that "at some juncture they end up taking a different course."