"There are important differences that we have, both practically as well as our vision for our respective countries and our conduct in foreign policy," Obama said.

"But what I've been very encouraged by is your willingness, Mr President, to engage in constructive dialogue."

In response, Xi said that their common interests outweighed their discord and he hoped that both sides would handle their disagreements through dialogue.

Human rights have long been an area where Washington and Beijing have been at odds. Obama said he broached the topic with Xi, saying universal freedoms were essential "whether it is in New York or Paris or Hong Kong". Xi, in response, said China was willing to engage with the US over the issue and seek a constructive way forward.

Xi insisted China had made "enormous progress" on human rights. "That is a fact that is recognised by all people in the world," he said.

While Obama is trying to consolidate US influence in the region with his "pivot to Asia" strategy, Xi has shown his determination to make China the region's pre-eminent military and economic power.

Relations have suffered over the past year, particularly over China's increasingly assertive approach to maritime territorial disputes with Japan and the Philippines - both US allies. Beijing has been sceptical of Obama's efforts to bolster US influence in the region, believing the strategy is aimed at containing China's rise.

However, Xi said "the Pacific Ocean is broad enough" to accommodate both the US and China.

Trade rivalries between the world's two largest economies were also apparent as they both championed their own free-trade pacts at the Asia-Pacific Economic Conference summit in Beijing earlier this week.

On the sidelines of Apec, China led the initiative on the Free Trade Area of the Asia-Pacific, while Obama hosted negotiations on the US-led Trans-Pacific Partnership, which excludes China and Russia, at the US embassy in Beijing.

OVER TO YOU MR PRESIDENT – THOUGHTS FROM THE TWO LEADER

"What I've been very encouraged by is your willingness, Mr President, to engage in an honest and constructive dialogue around those differences and ensuring that we manage them in a peaceful and effective way."

"I am always working on the assumption that the press gives me a hard time wherever I go, whether in the United States or China."

"Our two countries have enormous stakes in each other's success."

"A strong cooperative relationship with China is at the heart of our pivot to Asia."

"On the question of human rights, we should never consider our work to be a mission accomplished. It's always a work in progress. And there's always room for improvement."

"China upholds the principle of openness and inclusiveness in the proposals and initiatives it has raised, such as the new security concept for Asia and the establishment of the Asian Infrastructure Investment Bank and the Silk Road Fund."

"It goes without saying that law and order must be maintained according to the law in any place, not just in Hong Kong but also elsewhere in the world."

"The Pacific Ocean is broad enough for both China and the United States."

"Media outlets need to obey China's laws and regulations. When a car breaks down on the road, perhaps we need to get out of the car to see where the problem lies. And when a certain issue is raised as a certain problem, there must be a reason."

"When China and the United States work together, we can become an anchor of world stability and a propeller of world peace."