The Extinction Rebellion protesters were arrested and bundled into a mobile "custody unit" on Monday afternoon after they allegedly failed to move on when asked to do so by police.

Police say 30 people were arrested. Organisers say four girls aged under 16 were among them.

"Alleged offences committed range from obstructing traffic to disobeying reasonable direction," NSW Police said in a statement.

Assistant Commissioner Mick Willing said police respected the right of groups to protest but "we have a responsibility to the community and local businesses to ensure they can go about their normal activities without being impacted on or put at risk".

"Unfortunately, despite the warnings issued by local police and our colleagues from across the country, this group continue to set out to break the law and put themselves and others at risk," Mr Willing said in a statement.

Hundreds of people marched from Belmore Park along Pitt Street before several protesters locked themselves in a fake water tank on Broadway.

Sisters Luka, 10, and 12-year-old Maddie Brett-Hall alongside Ember Henninger, also 10, from the Blue Mountains were angry at being told by the government to "just be kids" but who felt their voices weren't being heard.

Extinction Rebellion media spokesman David Kohn, who was among those arrested, said climate action needed to be taken worldwide.

"We're demanding the government declare a climate emergency," the 28-year-old said.

"We want them to take climate action now; we want zero emissions by 2025 and we want citizens' assemblies to guide that transition."

Australian writer Jeff Sparrow compared the Extinction Rebellion protests to the Greensboro sit-ins in the United States in the 1960s against segregation during the American civil rights movement.

Sparrow told the crowd scientists' warnings on climate change meant silmultaneous "massive disruption" was needed.

"We need disruption of our transport system, we need disruption of our housing system, we need disruption of the economy to move it into a carbon-neutral phase."

Australian Associated Press