Presidents Barack Obama and Xi Jinping met for the final time Saturday, with the Chinese leader warning the period after Donald Trump's election is a "hinge moment" in relations between the two powers.

Without referring to Trump directly, Xi spoke of his hope for a "smooth transition" in a relationship that Obama described as "the most consequential in the world."

The two men were meeting in Lima, Peru on the margins of an Asia-Pacific Economic Cooperation (APEC) summit.

During a vitriol-filled election campaign Trump frequently took a combative stance against China, blaming Beijing for "inventing" climate change and rigging the rules of trade.

The White House, surprised by Trump's lack of details on the issues, has urged world leaders to give Trump time to get his feet under the desk.

For much of Obama's presidency, China and the United States have slowly improved cooperation and tried to limit the fallout from disputes, all while vying for influence in the Asia-Pacific.

China has been quick to seize on the failure of a US-backed Pacific trade deal to push its own version of the pact -- excluding Washington at the APEC meeting.

Xi -- who the White House sees as perhaps the most powerful Chinese leader since Deng Xiaoping or even Mao Zedong -- said he wanted to see cooperation continue.

"I hope the two sides will work together to focus on cooperation, manage our differences, and make sure there is a smooth transition in the relationship and that it will continue to grow going forward."

The two men have met nine times since Obama took office in early 2009.

Obama said he wanted to "take this opportunity to note our work together to build a more durable and productive set of bilateral ties."

"I continue to believe that a constructive US-China relationship benefits our two peoples and benefits the entire globe," he said at the start of the meeting.

"We've demonstrated what's possible when our two countries work together," he said, citing an agreement to tackle climate change.

- Areas of tension -

Obama also acknowledged that his eight years guiding US-China relations have seen difficulties.

That period has seen tensions in particular over China's seizure of territory it claims in the South China Sea, as well as over the treatment of US firms in China.

Obama said he expected a "candid conversation on areas where we continue to differ, including the creation of a more level playing field for our businesses to compete, innovation policies, excess capacity and human rights."

One area of continued tension concerns how hard to push sanctions against North Korea over its ballistic and nuclear weapons programs.

Obama said he and Xi "are united on our strong opposition to North Korea's provocations, and we will intensify our efforts to de-nuclearize the Korean peninsula."

The US is pushing for further sanctions to choke off funding to North Korean weapons programs.

Pyongyang has launched multiple tests to develop a miniaturized nuclear warhead and a missile capable of delivering that deadly payload to the United States, alarming the White House.

Beijing has long dragged its heels on sanctioning its allies in Pyongyang, fearing a flood of refugees if North Korea's economy collapses.

But earlier this year Beijing moved to sanction a conglomerate based in China's frontier city of Dandong that did an estimated $530 million in trade with North Korea between 2011 and 2015.

Obama has looked to his National Security Advisor Susan Rice -- who backpacked around China in the late 1980s -- to guide much of the relationship.

The White House points to some tangible progress from those efforts, including tying China to limited norms on cybersecurity after a series of hacking scandals and measures that increased the number of Chinese visitors to the United States.

"There is real value in, first of all, more engagement with China, more diplomacy, more channels and multifaceted discussions. And often, not always, that can yield progress," Rice told AFP ahead of the meeting.