Beijing has taken an increasingly firm tone over the protests, accusing foreign countries, including the United States, of inciting unrest. China's embassy in Ottawa also warned Canada to stop meddling in Hong Kong's affairs.
Hong Kong is gearing up for more protests this week after hundreds of thousands of anti-government demonstrators braved heavy rain to rally peacefully on Sunday, marking a change to what have often been violent clashes.
Sunday's turnout of an estimated 1.7 million people, according to the rally's organisers, showed that the movement still has widespread support despite chaotic scenes last week when protesters occupied the Chinese-ruled city's airport. Some activists have apologised for events at the airport.
The protests began more than 11 weeks ago as opposition to a now-suspended bill that would have allowed suspects to be extradited to mainland China for trial in Communist Party-controlled courts and have since swelled into wider calls for democracy.
Hong Kong returned from British to Chinese rule in 1997 under a "one country, two systems" formula that promised wide-ranging freedoms denied to citizens in mainland China, but many in the city believe Beijing has been eroding those freedoms.
The protests have presented one of the biggest challenges for Chinese President Xi Jinping since he came to power in 2012.
Further demonstrations are planned in coming weeks, including another strike in districts across the city.
Police said on Monday that, while Sunday's demonstration was mostly peaceful, acts of breaching public peace happened later when some protesters damaged government offices and aimed laser beams at police officers.
Protesters spilled out from Victoria Park, the designated rally area on Hong Kong island, on Sunday and streamed onto major thoroughfares towards the city's financial centre, chanting for Beijing-backed leader Carrie Lam to step down.
However, the demonstrators dispersed and went home later on Sunday in a break from other recent protests that were marred by violent clashes with police.
The government said in a statement on Sunday night it was important to restore social order as soon as possible and that it would begin talks with the public and "rebuild social harmony when everything has calmed down".
Police have come under criticism for using increasingly aggressive tactics to break up demonstrations, but there was a minimal police presence on Sunday and no arrests were made.
More than 700 people have been arrested since the protests began in June.
The central government in Beijing has taken an increasingly firm tone over the protests, accusing foreign countries, including the United States, of inciting unrest.
US President Donald Trump hinted on Sunday that the White House would like to see Beijing resolve the protests before the world's two largest economies could reach a trade deal.
"I would like to see Hong Kong worked out in a very humanitarian fashion," Trump said. "I think it would be very good for the trade deal."
Trump also warned China on Sunday that carrying out a Tiananmen Square-style crackdown on Hong Kong pro-democracy protesters would harm trade talks between the two countries.
"I think it'd be very hard to deal if they do violence, I mean, if it's another Tiananmen Square," Trump told reporters in New Jersey. "I think it's a very hard thing to do if there's violence."
China warns Canada to stop meddling in Hong Kong
China's embassy in Ottawa warned Canada on Sunday to stop meddling in Hong Kong's affairs, saying that "the Canadian side should be cautious with its words and deeds."
Canada and the EU issued a joint statement Saturday saying the right of peaceful assembly is enshrined in basic law in Hong Kong.
The statement from the Chinese embassy in Ottawa says the "people of Hong Kong enjoy unprecedented democratic rights and a broad range of freedoms rarely seen across the world."
It also says the "relevant protests and demonstrations in Hong Kong have already deteriorated and evolved into extreme violence. In face of such severe violence and offences, no government with a sense of responsibility would sit idly by."
If Canada wants to voice a position, the statement added, it should "clearly condemn the violent criminal activities."
Relations between both countries have been at their worst since the Tiananmen Square massacre in 1989, following Canada's arrest of a Chinese tech executive who is facing fraud charges in the US.
China has detained two Canadians in apparent retaliation.
The Chinese Communist Party's official People's Daily newspaper also warned again in an editorial on Monday that hostile foreign influences were inciting the protest movement.
It also said the protests carried a distinctive feature of "colour revolution", a reference to popular uprisings in former Soviet states, such as Ukraine, that often swept long-established rulers from power.
The central government has sought to deepen integration between the mainland and the special administrative regions of Hong Kong and nearby Macau. The State Council called on Monday for greater development of the so-called Greater Bay Area and to enrich the "one country, two systems" policy.
China has also put strong pressure on big companies, such as Cathay Pacific. Chief executive Rupert Hogg quit in a shock move last week after Beijing targeted the airline over the involvement of staff in the protests.
Hogg's sudden departure was announced by Chinese state television on Friday and was seen as a signal to other multinationals, such as HSBC Holdings and Jardine Matheson Holdings, to support Beijing.
Cathay also fired two pilots for engaging in the protests.
Shares in Cathay rose more than 2 percent early on Monday before paring gains to be down 0.6 percent. Jeffries analysts wrote in a note on Monday that it maintained its "buy" rating on Cathay and that it expected the company to remain profitable.
Asian shares rise as investors watch trade war, economies
Asian shares were higher Monday, as investors continue to rejigger their read on President Donald Trump's trade war and growing worries about slowing economies around the world.
Japan's benchmark Nikkei 225 rose 0.6 percent in early trading to 20,532.95. Australia's S&P/ASX 200 gained 0.8 percent to 6,454.40, while South Korea's Kospi was 0.4 percent higher at 1,934.78.
Hong Kong's Hang Seng rose 0.9 percent to 25,734.22. The Shanghai Composite added 0.3 percent to 2,823.82.
On Friday, the S&P 500 rose 41.08 points, or 1.4 percent, to 2,888.68.
The Dow, which had an 800-point drop earlier in the week, added 306.62 points, or 1.2 percent, to 25,886.01.
The Nasdaq climbed 129.38 points, or 1.7 percent, to 7,895.99. Each index still finished with a third-straight weekly decline.
Investors favored smaller company stocks, which pushed up the Russell 2000. The index rose 31.99 points, or 2.2 percent, to 1,493.64.
Wall Street stocks and other investments had heaved and dropped all week, hitting a crescendo on Wednesday when a fairly reliable warning signal of recession flipped on in the US Treasury market.
Investors are hoping that the Federal Reserve will continue to cut interest rates to shore up economic growth.
The central bank lowered interest rates by a quarter-point at its last meeting. It was the first time it lowered rates in a decade.
"With global economic engines still clattering and in desperate need of some high-grade Central Bank stimulus, investors are still pinning their hopes on central bank policy," said Stephen Innes, managing partner at Valour Markets in Singapore.
Investors are also worried about Trump's shocking announcement on August 1 that he planned to extend tariffs across virtually all Chinese imports, many of them consumer products that were exempt from early rounds of tariffs.
The tariffs have been delayed, but ultimately will raise costs for US companies bringing goods in from China.