* HK leader sends condolences to Liu Xiaobo's wife and family
* HK leader pledges to defend Hong Kong's core interests
* Lam acknowledges concerns over individual incidents (Wraps up interview and expulsion of legislators)
HONG KONG, July 14 (Reuters) - Hong Kong Chief Executive Carrie Lam said on Friday she shares the compassion of people over the death of Chinese dissident Liu Xiaobo and acknowledged "anxieties" about "incidents" in the former British colony.
Lam was speaking in her first interview with the international media since she was sworn in as the city's new leader by Chinese President Xi Jinping on July 1.
"Hong Kong people are always very compassionate and so I share that compassion of many Hong Kong people by sending my condolence to the wife and the family of Mr. Liu," said Lam.
Liu Xiaobo, who won the Nobel Peace Prize in 2010 for his efforts to promote democracy in China, died on Thursday at the age of 61 of multiple organ failure.
Hong Kong, a former British colony, returned to Chinese rule in 1997 and enjoys wide-ranging freedoms not granted in mainland China and an independent judiciary under a so-called "one country, two systems" arrangement.
But the abduction by mainland agents of Hong Kong booksellers, and Beijing's efforts to disqualify democratically elected, pro-independence lawmakers in the local legislature, have rattled confidence in that arrangement.
In a wide-ranging interview, Lam acknowledged concerns about certain "individual incidents" in the city, and said it was her duty to accurately reflect them to the central government in Beijing.
"I would say there are worries, there are anxieties, there is a strong perception over individual isolated incidents, but unless you've got evidence to prove there are clear breaches then it will remain at the level of anxieties and perception," Lam said, without elaborating.
Britain called the bookseller incident a "serious breach" of the Joint Declaration -- the 1984 treaty that paved the way for Hong Kong's 1997 return to China -- and said one of them, Lee Bo, had been removed from Hong Kong "under duress".
Hong Kong's high court on Friday removed four opposition lawmakers from the city's legislative assembly for failing to sincerely take the oath of office in a significant blow to the opposition.
Lam said she wouldn't intervene in the case.
XI'S HARDER LINE
Xi took what some saw as an explicitly harder line about Hong Kong's future during his visit marking the 20th anniversary of the financial hub's return from British to Chinese rule.
Xi warned in a speech that any attempt to endanger Chinese sovereignty and security, challenge its power, or use Hong Kong to carry out infiltration and sabotage activities would be acts that cross "the red line" and are "absolutely impermissible".
Lam, however, pledged to stand up for Hong Kong's core values if they were undermined, and stand by the people of Hong Kong in protecting their rights.
Hong Kong was also promised universal suffrage as an "ultimate aim" but Beijing has so far resisted granting a direct vote for a city leader with open nominations of candidates.
Over the past two decades, Hong Kong's "one country, two systems arrangement" has come under considerable strain, as the city's opposition forces have agitated for full democracy and railed against creeping Chinese interference in various sectors including business, politics, media, law and education.
The 60-year-old Lam, a devout Catholic, has said she hopes to lead Hong Kong "towards new glory" in the next five years and to heal unprecedented social divisions that have continued to fester since the massive 2014 pro-democracy Occupy protests that blocked major roads in Hong Kong for 79 days.
(Reporting by Martin Howell, editing by Bill Tarrant)