William's trip to China is the first since Queen Elizabeth and her husband Prince Philip paid a visit in 1986, and follows some sparring between London and Beijing over last year's pro-democracy demonstrations in the former British colony of Hong Kong.
Meeting in Beijing's cavernous Great Hall of the People, William handed over an official invite from the queen for Xi make a state visit to Britain. Xi is expected go to London later this year for a visit that could include a stay at Buckingham Palace.
"The British royal family has great influence not just in Britain but across the world," Xi told William, having asked first about his wife and the new child they are expecting.
"Over many years the British royal family has shown interest in and support for the China-Britain relationship and members of the royal family have done a lot and positively contributed to exchanges and cooperation between our two countries," he added.
William, Queen Elizabeth's grandson and second-in-line to the throne, told Xi that he looked forward to the rest of his trip, which includes commercial capital Shanghai and an elephant sanctuary in the southwestern province of Yunnan.
"It's been a long interest of mine for many years to come and visit China," William said.
He also asked about Xi's interest in soccer - Xi is a keen football fan - but reporters were ushered from the room before William finished speaking.
William is not being accompanied by wife Kate, who is due to give birth to the couple's second child in April.
William's father Prince Charles was among dignitaries at the handover of Hong Kong to Chinese rule in 1997 under a "one country, two systems" formula that gave it a wide degree of autonomy from the mainland.
Despite London and Beijing arguing of late about Hong Kong, many aspects of Britain are regarded positively in China.
The private British education system is popular with China's wealthy elite - the son of jailed former top politician Bo Xilai went to a British public school for example - and British television shows like Downton Abbey are also widely watched, albeit on illegal downloads and pirated DVDs.

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