Hong Kong (CNN) The detention of Hong Kong booksellers in China is not an issue the city's government should take up, its incoming leader said Thursday.

"It would not be appropriate for us to go into the mainland or challenge what happens on the mainland," said Carrie Lam, who will be sworn in July 1 as the next Hong Kong chief executive

Hong Kong's government is duty bound to safeguard its own situation under the principle of "one country, two systems" -- by which the city retains certain autonomy and freedoms -- but Lam told CNN that the bookseller case "has to be dealt with in accordance with the mainland's system."

Missing booksellers

The disappearance of five Hong Kong booksellers almost two years ago sparked outrage and protests in the city amid concerns over the erosion of the rule of law and China's encroachment on Hong Kong's autonomy.

All five were associated with publisher Mighty Current, which has put out books critical of Chinese President Xi Jinping and other leaders.

One of the men, British citizen Lee Bo, was "involuntarily removed" from the city and taken to China, according to the UK . He later denied he had been abducted , saying he went to China to help in the investigation into his colleague Gui Minhai, a Swedish citizen who disappeared from his home in Thailand in October 2015.

Gui dramatically re-emerged on Chinese state-controlled television months later, apparently owning up to a 2003 hit-and-run accident in what supporters said was a forced confession.

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Lam Wing-kee, whom Chinese police seized after crossing the border from Hong Kong to Shenzhen, China, told CNN he was kept for months in solitary confinement and forced to confess to distributing books banned in China.

He later fled during a one-day release to Hong Kong in which he was meant to gather evidence against himself. But instead he went public with his story.

Gui remains in custody somewhere in China, and members of his family said they have been denied access to him, as have Swedish consular officials and his attorneys.

Speaking out

The UK is a signatory to the Sino-British Joint Declaration under which the former British colony of Hong Kong was guaranteed certain protections and basic human rights.

Last year, London said the booksellers case represented a "serious breach" of the agreement, sparking an angry response from Beijing , which accused British officials of repeating "unwarranted accusations."

"China is more and more regarding Hong Kong as part of China politically, even though the Sino-British Joint Declaration is supposed to protect against precisely this," Angela Gui told CNN.

"What happened to my father and his colleagues shows really blatantly how China ignores the treaty."

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In November, PEN America, which lobbies for free speech rights worldwide, said the bookseller case was indicative of how the international community does not stand up to China on issues of human rights.

A spokeswoman for the Foreign Office told CNN the UK "takes our longstanding commitment under the Sino-British Joint Declaration very seriously. Hong Kong's success relies on the rights and freedoms protected by that international treaty, including the rule of law and an independent judiciary."

Angela Gui said that Hong Kong's leaders have also not done enough, and she was critical of Lam for referring "to the rule of law and 'one country, two systems' to excuse politically motivated kidnappings."

"The kidnappings of my father and his colleagues have everything to do with 'one country, two systems': They are a painfully obvious breach of it," she said. "As this has implications for the security of all Hong Kongers, one would have thought that the chief executive would be more concerned."

Carrie Lam said that while she "sympathizes" with Angela Gui's situation "at the end of the day we must respect the rule of law in respective jurisdictions."

Handover concerns

As Hong Kong prepares to mark 20 years of Chinese rule next month, the booksellers case looms large, Amnesty International researcher Patrick Poon said.

"People in Hong Kong, especially those working on sensitive issues, are still worried about their safety," he said. "Nobody can guarantee that something like Lee Bo's case won't happen again."

Poon pointed to the case earlier this year of Chinese billionaire Xiao Jianhua, who was seized in a Hong Kong hotel and taken to China.

Artist and activist Kacey Wong said the booksellers case was a "game changer," leaving him and many others feeling like "anything can happen."