This month, China's official Xinhua news agency unveiled some of the law's provisions, including that it would supersede existing Hong Kong legislation and that interpretation powers belong to China's parliament top committee.
She said the law, which is expected to come into force imminently, would not undermine the city's autonomy or its independent judiciary.
"We hope the law will serve as a deterrent to prevent people from stirring up trouble", Tam said.
"Their aim is to govern Hong Kong through fear from this point forward", Rosenzweig said.
Hong Kong stocks were up 0.9% on Tuesday, in line with Asian markets.
Benedict Rogers, a co-founder of Hong Kong Watch, called for the appointment of a United Nations special envoy/rapporteur on Hong Kong, the passing of targeted sanctions against the perpetrators of human rights abuses, the formation of an global contact group to monitor the situation on the ground, and the coordination of an worldwide life-boat policy "to help Hongkongers in need of a lifeline".
Hong Kong was upended by seven straight months of protests previous year, initially sparked by an eventually abandoned plan to allow extraditions to the mainland.
Hong Kong activist Joshua Wong said on Tuesday he is stepping down as leader of his democracy group Demosisto, just hours after local media reported that Beijing had passed national security legislation for the Chinese-ruled city.
He said the fact that the law had been passed without anyone in Hong Kong seeing the full text suggested it would be used as a "weapon of repression" against peaceful opposition and criticism.
Demosisto then announced on Facebook it was disbanding, saying the loss of top members made it hard to continue.
What it says: The law defines crimes such as terrorism and sedition broadly, but mandates harsh sentences - in many cases life imprisonment - for those found to have committed them.
The US will end the exports of US-origin defense equipment to Hong Kong, Secretary of State Mike Pompeo announced Monday, citing the need to protect American national security as the tensions between the US and China continue to escalate.
Zhao, the foreign ministry spokesman, warned that the United States "should not review, advance or implement relevant negative bills concerning Hong Kong, even less impose so-called sanctions on China, otherwise China will firmly take strong countermeasures".
Yet, there are no terrorists in Hong Kong who threaten anyone's "national security", let alone that of China.
Henry Tang, a member of the standing committee of the advisory body Chinese People's Political Consultative Conference, told reporters that China will only exercise jurisdiction on a minority of cases that the Hong Kong government has "no ability, no power or no authority" to handle.
"We can not risk these items falling into the hands of the People's Liberation Army, whose primary goal is to uphold the dictatorship of the CCP by any means necessary", he said, referring to the Chinese Communist Party.
Washington - which has embarked on a trade war with China - has said the security law means Hong Kong no longer enjoys sufficient autonomy from the mainland to justify special status.
The law will apply to permanent and non-permanent residents of Hong Kong.
Hong Kong leader Carrie Lam said on Tuesday that this will have minimal impact on the city.
Similar national security laws are used on the authoritarian mainland to crush dissent, in particular the more vaguely worded subversion and collusion offences. Xi Jinping signed the law on Tuesday.
In addition, Hong Kong, with an adviser appointed from Beijing, will reportedly have to set up its own national security commission to enforce the laws.
Al Jazeera's Katrina Yu, reporting from Beijing, noted the passage of the law had been fast-tracked. "Hong Kong people, see you all in the streets".
Chinese officials have railed against what they claim is deep-seated foreign interference in the territory that they blame for encouraging last year's anti-government protests. Instead the news filtered out via pro-Beijing politicians and local media outlets in Hong Kong.
Beijing denies stifling Hong Kong's freedoms and has condemned Tsai's offer.
Beijing and Hong Kong's government reject those allegations.
However many are also wary of incurring Beijing's wrath and losing lucrative access to the mainland's huge economy.