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It is the third time Prince William has spoken on the subject in the past year.
Calling on China to help save endangered animals, he also highlighted how previous generations of the Royal Family had “little concern” about acquiring ivory.
President Xi Jinping has arrived in the UK on a four-day state visit.
Prince William, who has worked at forging a relationship with China, recorded his speech for the Chinese state TV channel CCTV1.
He raised the issue with Mr Xi when they met in Beijing earlier this year and his broadcast will form part of a series of programmes called Let’s Talk.
China imposed a one-year ban on the import of ivory in February, amid criticism that demand among Chinese consumers is fuelling poaching in Africa.
The Born Free Foundation, a wildlife charity, says “tens of thousands” of elephants are killed for their ivory every year.
The prince said that if African elephants continued to be killed at the current rate of 54 a day, there would be none by the time his daughter, Princess Charlotte, was 25.
“My rejection of ivory today is not a judgement of past generations. It is an acceptance of the world as I find it today and the world I want my children, George and Charlotte, to inherit,” he said.
“Likewise, those doctors and medical practitioners in China that are speaking out against the use of endangered species in medicine, they are not judging previous generations who did not have the facts that you do today.
“They are just accepting the truth that all credible evidence and scientific research shows, for example, that rhino horn cannot cure cancer.”
Image copyrightReutersImage captionThis week’s is the first state visit by a Chinese president since 2005
Large red flags of the People’s Republic of China are lining The Mall in central London, along with the union jack, in preparation for Mr Xi’s official welcome on Horse Guards Parade.
The Communist leader and his wife Peng Liyuan arrived at Heathrow Airport and were greeted on behalf of the Queen by Viscount Hood.
During their visit they will meet with the Queen and Prime Minister David Cameron, visit businesses and address members of the Houses of Parliament at Westminster.
Who is China’s President Xi?
Born in Beijing in 1953
Son of Xi Zhongxun, a revolutionary who helped to found the People’s Republic of China
Father purged in 1962, Xi sent to work in a remote village aged 15
Joined Communist Party in 1974
Became party chief of Shanghai in 2007
Communist Party leader since 2012
Married to actress and singer Peng Liyuan since 1987
Amnesty International and other groups concerned with human rights issues in China are expected to protest in St James’ Park on Tuesday and it is expected that there will also be a pro-China protest.
Mr Cameron, in an interview with CCTV1, said Mr Xi’s visit was a “very important moment” and hailed a “golden era” in ties between the countries.
Chancellor George Osborne said on his return from a week-long visit to China last month that it was the government’s intention to make the UK China’s “best partner in the west”.
China state visit: The timetable
Image copyrightReutersImage captionChina’s President Xi Jinping will arrive in the UK with his wife Peng Liyuan on Monday evening
President Xi and his wife Peng Liyuan receive a ceremonial welcome at Horse Guards Parade before travelling in a carriage procession along The Mall to Buckingham Palace
Later, Mr Xi will address the members of the Houses of Parliament
The president is due to meet Labour leader Jeremy Corbyn
The Queen will give a state banquet at Buckingham Palace
Mr Xi will visit Imperial College London with the Duke of York and the Chancellor George Osborne
He will meet with David Cameron at Downing Street before before visiting the UK-China Business Summit at Mansion House and then Chinese telecommunications company Huawei Technologies
Mr Xi, joined by the Duke of York, will visit Inmarsat, a global satellite communication services company, before attending a Confucius Institute conference hosted by UCL Institute of Education
In the evening, Mr Xi and Ms Peng will join Mr and Mrs Cameron at Chequers for dinner before flying to Manchester
Mr Xi will visit the National Graphene Institute at the University of Manchester with Mr Osborne and then the City Football Group with Mr Cameron
The president and Mr Cameron will attend an event at Manchester Airport before Mr Xi and Ms Peng depart