Suspects arrested by China's new office in Hong Kong on charges of violating the city's new national security law could be tried in the mainland, a senior Chinese government official said on Wednesday.

The office abides by Chinese law and Hong Kong's legal system cannot be expected to implement the laws of the mainland, said Zhang Xiaoming, Executive Deputy Directors of the Hong Kong and Macau Affairs Office.

Read more: China's security law: The end of Hong Kong's semi-autonomous status?

The law, he added, would not be applied retrospectively. "This law is a birthday gift to [Hong Kong] and will show its precious value in the future," Zhang said.

Under the law, Article 55 says that China's national security office in Hong Kong could exercise jurisdiction over "complex" or "serious" cases.

Additionally, a Hong Kong police spokesman said that people who display pro-independence material will face arrest and prosecution under the new law.

The announcement comes a day after China approved the security law, which aims to punish secession, subversion, terrorism and collusion with foreign forces.

Under the new law, mainland security agencies will be based in Hong Kong for the first time officially, giving Beijing powers that extend beyond the city's local laws.

At the same press conference, Zhang rebuffed international criticism of the law, saying, "What's this got to do with you? It's none of your business."

He also said that the law was not meant to undermine Hong Kong's autonomy. "If what we want is one country, one system, it would have been simple," he said. "We are completely able to impose the criminal law, the criminal procedure and the national security law and other national laws on Hong Kong."

"Why would we need to put so much effort into formulating a national security law tailor-made for Hong Kong?"

Far-reaching legislation

Critics of the law have noted that it has a far-reaching application, and would allow for the arrest of people who violated the law outside of Hong Kong.

The law "has a very wide-ranging extra-territorial effect, which even goes beyond what the PRC system normally allows," Eric Cheung, a professor at the University of Hong Kong Law School told DW. "We can see that basically this new legislation can punish conducts which happened outside Hong Kong."

If a suspect is always outside of Hong Kong, authorities do not have very much power to do anything. "However, once the suspects set foot on Hong Kong's land, including transiting, in theory, the suspects can be arrested and prosecuted under the new law," said Cheung.

"This is really alarming that the law even put people outside Hong kong at risk of commiting crime under the new legislation,"  he added.

First arrests made

Hong Kong police moved to stop protesters gearing up for the first rally since the introduction of the law, while also making their first arrests under the new measure.

The first suspect to be arrested, the Hong Kong police tweeted, was held for holding a pro-independence flag at a rally to mark the 23rd anniversary of the former British colony's handover to China.

Police also said they arrested 30 people for unlawful assembly, violating the security, obstructing police and possessing weapons. 

One metro station was closed, while officers used pepper spray as thousands gathered downtown for the demonstration. 

Police, who earlier banned the protest, cited the new law when confronting protesters. "You are displaying flags or banners/chanting slogans/or conducting yourselves with intent such as secession or subversion, which may constitute offenses under the national security law," read an official message displayed on a purple banner. 

Read more: China's Hong Kong security law sparks global outcry

Critics have said that the security law marks the end of Hong Kong's remaining autonomy.

The law also stipulates a ban on violators of the law standing for election, and greater oversight of non-governmental organizations and newsgroups.

Read more:Opinion: China to rule Hong Kong by fear with new national security law 

The security office will "take necessary measures to strengthen the management of and services for organs of foreign countries and international organizations in the region, as well as non-governmental organizations and news agencies of foreign countries," Article 54 of the law says.

Hong Kong's Chief Executive Carrie Lam praised the move, saying it was an "inevitable and prompt decision to restore stability in the society."

Beijing has said the law is aimed at just a few "troublemakers" and will not affect rights, freedoms or investors' interests. Some pro-China officials have said the law is aimed at sealing Hong Kong's "second return" to the mainland. The legislation came into force at 11pm local time (3pm GMT) on June 30.

lc/stb (Reuters, AFP)