U.S. Secretary of State John Kerry said on Friday he had "very positive" talks with Chinese President Xi Jinping on specific problems involving North Korea and the future of Washington-Beijing ties. Speaking to Chinese Foreign Minister Wang Yi at his office, Kerry said his meeting with Xi was "very constructive and positive."    "I'm glad we had an opportunity to dig into the detail of some of the North Korea challenges," the secretary said. He did not elaborate, as he made the opening remarks in front of reporters. Right after flying to Beijing, Kerry met with Xi at the Great Hall of the People. Xi also "outlined important guiding principles for the further growth" of the China-U.S. relationship, according to the Chinese minister. Wang emphasized that Beijing and Washington need to improve their ties on agreed-upon principles to "respect each other's core interests and major concerns."    Before going into a closed-door session, the top diplomats of the two global powers also exchanged friendly words. They were meeting on Valentine's Day and China's traditional Lantern Festival fell on the same day. Wang noted, "Today is the last day of the Lantern Festival," which officially marks the end of Chinese New Year celebrations. He expressed hope that the China-U.S. relationship would get off to a good start. But the two sides face a host of thorny issues. The Obama administration seeks to prod Beijing to do more for the denuclearization of North Korea. On his trip to Seoul, Kerry said China has a "unique role" to play for that, given its political and economic influence over the communist ally. The U.S. is also encouraging China to peacefully settle its territorial rows with Japan and a number of Southeast Asian nations. U.S. officials are apparently concerned about China's growing assertiveness in the territorial disputes. They do not rule out the possibility of military clashes in the region. Tensions between China and Japan have soared over a set of Tokyo-controlled islands in the East China Sea. In the South China Sea, Vietnam, the Pilippines, Taiwan, Malaysia, Brunei and China are involved in long-standing sovereignty disputes over a potentially oil- and gas-rich island chain. A senior U.S. official said, "Our consistent and clear position is that these issues of territorial sovereignty and maritime sovereignty must be dealt with through peaceful diplomacy, through non-coercive means," a senior U.S. official said in a background briefing for reporters that took place in Kerry's plane earlier this week. On Saturday, meanwhile, Kerry plans to fly to Jakarta, Indonesia.