Xi said next year marks the 40th anniversary of the establishment of diplomatic ties between the United States and China, adding that China attaches great importance to the development of bilateral relations and appreciates the willingness of the USA side to develop cooperative and constructive bilateral relations. If made, it will be very comprehensive, covering all subjects, areas and points of dispute.
Trump said on the call that the talks and consultations with China were achieving positive progress, and that he hoped to reach results that benefit China, the United States, and the world, according to Xinhua.
Carter, who has devoted his post-presidential career to eradicating poverty, said that the "easiest route" to cooperation between the U.S. and China was in Africa.
"I hope that the two teams will meet each other half way, work hard, and strive to reach an agreement that is mutually beneficial and beneficial to the world as soon as possible", Xi said to Xinhua news agency.
"History has proved that cooperation is the best choice for both sides", Xi said, adding that Sino-US relations were at an important stage.
The countries - the world's two largest economies - have slapped tariffs on one another's goods, though Washington and Beijing agreed on December 1 to postpone further hikes in an effort to negotiate a deal that satisfies both sides.
Both leaders also extended New Year greetings to people from their respective countries, Xinhua said. In recent weeks, China has showed signs of some relaxation in its trade policies with the USA as it opened up its market for some American products. Trump has since demanded that U.S. taxpayers pay for it at an estimated total cost of $23 billion. Small signs of progress were seen and Trump didn't announce any fresh threats.
The US and China must and can align their economic and national security objectives, as this is essential for the two largest economies to peacefully coexist in the current century, said John Milligan-Whyte, chairman of the America-China Partnership Foundation in NY.More news: Juventus chief: We 'really like' Aaron Ramsey
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What's the background to the trade war?
Ties have improved dramatically from their Cold War nadir, though the two countries have since weathered ups and downs over a number of issues including Taiwan, human rights, and trade.
Xi Jinping. File photo: GovHK.
China has been locked in a bruising trade war with the United States and is also facing a slowing domestic economy.
The presidents both expressed "their willingness" to implement the agreements made at the start of the month over a steak dinner on the sidelines of the meeting of the G20 nations.
USA stocks, beaten down recently by concerns about an escalating tariff war, got a boost from news of the upcoming talks in Beijing.
"The Chinese and U.S. economic and trade teams have always maintained close communication", commerce ministry spokesman Gao Feng said at a regular briefing.
Foreign Ministry spokesman Lu Kang said last week that in developing China-US relations, the two sides should view each other's strategic intentions in a rational and objective manner, step up strategic communication, enhance strategic mutual trust and avoid misjudgment.
Resolving the bruising spat could help shore up confidence in the Chinese economy, which itself is bracing for a slowdown.