Hong Kong was a British colony until 1997, when it became a special administrative region of China under the "one country, two systems" framework which allows the territory a certain degree of legal and economic autonomy.

The march was set to take place from Chater Garden, in the central district of Hong Kong, to the central government office.

"It's time for us to stage a really civilized and calm march in the central business district to show that we're still not happy with how the whole issue has been handled, and (the) government has to respond positively to the demands of the people," Hong Kong legislator, Kenneth Leung, told CNBC on Friday, ahead of the march.

Accountants in Hong Kong took to the streets on Friday to call for the government to accept five demands of the people, including the complete withdrawal of a now-suspended extradition bill.

Accountants are particularly concerned about the extradition bill because they often have to cross over to mainland China for work, said Leung. The proposed extradition bill, which would have allowed fugitives to be handed over to authorities in mainland China, was suspended by the city's Beijing-backed Chief Executive Carrie Lam last month.

Lam has repeatedly said the extradition bill is "dead" but continues to refer to it as "suspended" instead of "withdrawn."

Other protesters have also called for the resignation of Lam, who has been blamed by the demonstrators for mishandling the situation.

Last week, state-owned tabloid Global Times said there have been calls for Hong Kong's top accounting firms to fire employees who were "pro-riot."

The Global Times TWEET: Top accounting firms urged to fire pro-riot staff

However, Leung said accountants were not at risk of losing their jobs. That's because these protests are "not straddling any red line" and it's "not threatening national sovereignty," he said. Rather, they are a freedom of expression protected by Hong Kong's laws, he added.

These accounting firms generate between 10% and 15% of their revenue from doing business in mainland China, so tensions between Hong Kong and China could pose a threat to their earnings, Leung said.

"Hong Kong and mainland China business is really their bread and butter, so they should be concerned. Of course, they do not want to be seen ... doing something against the so-called red line, which is national sovereignty," Leung said.