Hong Kong pro-democracy activists kept up the pressure on authorities on Saturday with a colourful "family rally" and a march staged despite police objections, as protests enter the third month.
The fresh demonstrations came after the financial hub's chief executive ruled out concessions, and as Beijing and Washington stepped up a war of words over a US diplomat's meeting with Hong Kong activists.
Beijing has taken a harsh line on the demonstrations but protesters remain unbowed, with a weekend sit-in at the airport also heading into its second day on Saturday.
Demonstrators across the city staged shows of public support for the movement, which began in opposition to a bill that would have allowed extradition to mainland China but has become a broader push for democratic freedoms.
Older residents joined "silver hair" rallies and hundreds of parents and children gathered for an all-ages family protest under the banner "guard our children's future".
Faye Lai attended with her three-year-old niece and said she hoped the demonstration would help children understand the recent tumult.
"Hong Kong's future is theirs. We are fighting for rights that children should have," Lai told AFP.
Many attendees held balloons and a leaflet was circulated featuring a "Hong Kong Protest ABC", offering "demonstration" for the letter D, and "protest" for P.
The colourful and calm atmosphere at the rally was a far cry from the increasingly violent confrontations that have marked recent protests.
Elsewhere in the city, protesters gathered in the Tai Po neighbourhood for a march despite police denying them a permit.
Hundreds of demonstrators, many wearing the movement's signature black and sporting helmets and face masks or respirators, chanted against officers in riot gear standing guard outside the local police station.
One policeman held up a blue sign warning: "This meeting or procession is in breach of the law. Disperse or we may use force."
Protesters have committed to continuing their rallies with Lam insisting she would not meet their demands, which include direct election of the city's leader and an investigation into police violence.
"I don't think we should just sort of make concessions in order to silence the violent protesters," Lam said on Friday.
"What is right for Hong Kong... is to stop the violence, and to say no to the chaotic situation that Hong Kong has experienced in the last few weeks, so that we can move on."
She warned that the protests were causing economic chaos -- an accusation that protesters in Tai Po dismissed.
"The protests were created by Lam, since the beginning," said a woman who gave only her surname, Lo.
"Every time she comes out she only condemns (protests), but offers no solution."
"If Hong Kong's political system regresses and becomes like the mainland, even without protests or chaos, it wouldn't be able to attract people to invest and do business," added a student, who gave only his surname, Chan.
Beijing has thrown its support behind Lam and warned protesters that "those who play with fire will perish by it".
China's aviation regulator on Friday ordered Hong Kong carrier Cathay Pacific to turn over information on staff working on mainland-bound flights, warning that all personnel involved with or supporting "illegal protests" would be banned from flying to the mainland or through Chinese airspace.
It was not clear how the ban would be enforced and there was no immediate reaction from the airline.
Beijing and Washington meanwhile traded barbs over an American diplomat's meeting with Hong Kong activists.
Washington on Friday accused pro-Beijing media of publishing "dangerous" reports that identified the diplomat's husband and children, and dubbed the Chinese response the behaviour of a "thuggish regime".
China's foreign ministry in Hong Kong meanwhile denounced the US State Department for "blatant slander" saying its comments had "again exposed US gangster logic".
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