But Trump has offered no clear prescriptions for the strategic issues that plague ties between the two powers.
In a telephone call, Xi told Trump -- who frequently savaged China on the campaign trail and threatened to impose a 45-percent tariff on Chinese-made goods -- that the world's top two economies "need cooperation and there are a lot of things we can cooperate on", CCTV reported.
Xi and Trump "vowed to keep close contact, build good working relations, and meet at an early date to exchange views on issues of mutual interest and the development of bilateral ties", CCTV said.
Before his election, Trump went as far as calling the Asian giant America's "enemy", accused it of artificially lowering its currency to boost exports, and pledged to stand up to a country he says views the US as a pushover.
He has vowed to pursue a policy of "peace through strength" and build up the US navy.
But he also indicated he is not interested in getting involved in far-off squabbles, and decried the proposed Trans Pacific Partnership (TPP) free trade deal, which encompasses several other Asian countries and has been seen as an effort to bolster US influence, for costing American jobs.
CCTV cited Trump as saying in the call that China was a large and important nation that he was willing to work with, and that he believed Sino-US relations could realise "win-win" benefits.
The phrasing the broadcaster attributed to the US president-elect is typical of Chinese diplomacy.
Trump's contrary and ambiguous positions have left a pall of uncertainty over how he will manage the relationship between the world's two largest economies and its biggest and most powerful militaries.
Under President Barack Obama, Washington's foreign policy "pivot" towards Asia was viewed with alarm in Beijing, which saw it as an attempt to contain its growing geopolitical and economic might.
But Trump has offered no clear prescriptions for the strategic issues that plague ties between the two powers, from Beijing's territorial claims in the South China Sea to North Korea's nuclear programme and the future of Taiwan.
He has also indicated America had had enough of paying to defend allies such as Japan and South Korea, even suggesting they should develop their own nuclear weapons.
Mark Williams of Capital Economics previously said in a note that "if the US is less engaged in Asia, Beijing will have an opportunity to shape regional political and economic integration on its own terms".
That could include an Asia-focused trade agreement of its own that excludes the US, in the same way that China was not part of TPP.
Beijing is already embarked on negotiations to create the Regional Comprehensive Economic Partnership (RCEP), a free trade area encompassing the Southeast Asian grouping ASEAN, China, India, Japan, South Korea, Australia and New Zealand.
Something of a mirror image to the TPP, it includes six of the putative Washington-led grouping's 12 members.
It would encompass more than three billion people and Australian Foreign Minister Julie Bishop told media Thursday that if the TPP does fail, "then the vacuum that would be created is most likely to be filled by RCEP".
Asked about Trump's tariff threat, China's foreign ministry spokesman Lu Kang told reporters last week that the 200-fold expansion in bilateral trade between the two countries in recent decades had been mutually beneficial.
"Any statesman in the US who has his people's and his country's interests in mind will make the right decision," he said.