Speaking at a news conference streamed live from her office by Channel News Asia, Lam claimed that her administration had no plans to use emergency powers and added: "I still strongly feel that we should find the solutions ourselves". "But I would appeal (to) everyone in society to join hands to achieve this objective".
Protesters are demanding Lam's resignation even after she withdrew legislation that provoked the latest rounds of turmoil.
Some students from La Salle College wear masks, which have been banned at protests under emergency powers, as they walk to school in Hong Kong on Tuesday.
The most recent protests followed warnings against opposition leaders who Lam's choice to invoke a colonial-era crisis law to inflict the mask ban could only anger protesters fighting for greater political freedoms, such as the right to select their leaders.
Dennis Kwok, a Civic Party member of the city's Legislative Council said the protest movement still enjoyed majority support despite the upsurge in violence.
Since last Friday, more than 200 shops and public utilities have been damaged in the unrest and the police have fired 367 tear gas rounds, said a police spokesman.
A riot police officer detains a demonstrator in Admiralty, Oct. 6.
The attack on Apple comes just one day after the Chinese government canceled a Brooklyn Nets event earlier this week and a Chinese state broadcaster reported that the country will no longer air preseason games played in China.
China has warned foreign governments to stay out of the protests which they deem as an "internal affair" and have accused some, including Britain and the United States, of fanning anti-China sentiment.
On Tuesday, Chinese activewear company Anta, which has endorsement deals with stars including Golden State Warriors guard Klay Thompson, announced it would halt contract renewal negotiations with the National Basketball Association.
The economy of Hong Kong, a vital global financial hub, has taken a beating during the months of protests, which have been exacerbated by the U.S.
The territory is facing its first recession in a decade.
The total number of visitors to Hong Kong was down 37 percent, to about 1.88 million.
A tenth of automated teller machines were broken due to vandalism.
She also called on the business communities, property developers and the society to do their part to help those affected to tide over the tough times together.
China has a garrison in Hong Kong where it stations personnel of People's Liberation Army (PLA).
But the city government has rejected accusations of excessive force.
HKmap.live, designed by an outside supplier and available on Apple Inc.'s online store, 'facilitates illegal behaviour, ' the newspaper said in a commentary.
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