Xi in turn told Japan's first woman prime minister, long seen as a China hawk, at the talks in South Korea that he hopes her government will have a "correct understanding" of his country, according to state media.
Takaichi has been a regular visitor to the Yasukuni shrine that honours Japan's war dead and is an outspoken backer of Taiwan, advocating security ties with the self-ruled island that China claims as its territory.
With both having separately met US President Donald Trump in recent days, Takaichi said she told Xi at the APEC summit that she wanted a "strategic and mutually beneficial relationship between Japan and China".
However, she told reporters that she also raised a number of thorny issues with the Chinese leader, saying that it was "important for us to engage in direct, candid dialogue".
"We... expressed serious concerns regarding actions in the South China Sea, as well as the situations in Hong Kong and the Xinjiang Uyghur Autonomous Region," Takaichi said.
Beijing vehemently denies accusations of human rights abuses against the Uyghurs, saying its policies in Xinjiang in northwestern China have eradicated extremism and boosted development.
China has sweeping assertions of sovereignty over the South China Sea despite an international ruling in 2016 concluding its claims have no legal basis.
Takaichi said she also raised with Xi the Japanese-administered Senkaku islands, known as the Diaoyu in China, in the East China Sea where Japanese and Chinese vessels frequently face off.
She also said she spoke to Xi about export controls on items including rare earths that are vital for a wide range of industries.
Takaichi added that she also pressed for the release of Japanese citizens detained in China and requested that the safety of Japanese expatriates in China be ensured.
"I conveyed that we would like these matters to be addressed," she said.
"Regarding Taiwan, there was some discussion from the Chinese side," Takaichi said.
"I stated that for the stability and security in this region, maintaining good cross-strait relations is important," she said.
- History -
Xi told Takaichi he hoped Japan would also stick to the "general direction of peaceful, friendly and cooperative bilateral relations", Chinese state news agency Xinhua reported.
He added that Japan "should adhere to and fulfil clear provisions on major issues such as history" as outlined in political documents agreed by Japan and China, Xinhua said.
Visits to the Yasukuni shrine in Tokyo by senior Japanese politicians have long angered China, as well as the two Koreas, because it also honours convicted war criminals.
Takaichi was also an acolyte of right-wing former premier Shinzo Abe.
Long-pacifist Japan, a close US ally, has increased security ties with Washington as well as defence spending, while moving to acquire "counter-strike" capabilities.
Around 60,000 US military personnel are based in Japan. Takaichi hosted Trump this week, with both making speeches on the deck of an American aircraft carrier.
She announced last week Japan would spend two percent of gross domestic product on defence this fiscal year, two years ahead of schedule.
"It could be a frosty get-to-know-you meeting as Xi Jinping has not sent a congratulatory message to Takaichi, wary of her reputation as a China hawk," Yee Kuang Heng, a professor at the University of Tokyo's Graduate School of Public Policy, told AFP before the meeting.
"Overall though, stability is a shared priority," Heng said.
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