Among other things, the central government wants Hong Kong to bring the 60 or so people charged under the legislation to justice, she said.
The majority of those charged under the law to date are opposition figures, and most of them are behind bars awaiting trial.
Lam said another task for her administration is to step up guidance and supervision of local schools, social organisations, the media and social media, in order to prevent acts that endanger national security.
The CE was speaking to reporters after listening to a speech by the head of the Hong Kong and Macau Affairs Office, Xia Baolong, who shared his views at a forum on the legislation, via video link from Beijing.
Xia was quoted as saying that he particularly wants the SAR government to do a good job in making sure only patriots are allowed to run in election committee, Legco and CE races.
He also reportedly told the audience, which included SAR officials and Beijing loyalists, that once the security law was imposed on Hong Kong last year, the results were swift and noticeable.
“Director Xia strenuously rejected the smearing of the law by Western politicians and media, who claimed Hong Kong’s status as an international financial centre will be undermined and there would be many problems,” Lam said.
She also agreed with Xia that the social unrest of 2019 had made everyone in society understand that Hong Kong could not tolerate gaping holes in national security and that the SAR government could no longer turn a blind eye to the problem.
Xia also praised the police and the Committee for Safeguarding National Security for doing a good job, Lam added.