SYDNEY (Reuters) -Thousands of people attended pro-Palestinian rallies in Australian state capitals on Sunday despite police threats to curb them, amid tensions after the bloody Hamas incursion into Israel eight days ago.

One of the largest rallies was in Sydney, the capital of the country's most populous state of New South Wales, where protest organiser, the Palestine Action Group, said around 5,000 attended. A Reuters witness estimated the crowd to be around 2,000.

Many rally-goers waved Palestine flags and chanted "Free, free Palestine" in Sydney's Hyde Park, as hundreds of police patrolled the area and nearby streets, and a police helicopter circled low overhead.

Police had been considering applying special stop-and-search powers for the first time in almost two decades for people attending the rally, but a Palestine Action Group spokesperson, Amal Naser, said the powers had not been deployed.

The rally was "peaceful so far", Naser said.

Pro-Palestine rallies were also being held on Sunday in state capitals Adelaide and Melbourne, where thousands protested, according to The Guardian Australia.

At the Sydney rally, attendee Ayah, a Palestinian living in Sydney, said she was there to "be peaceful, to support my country, nothing to do with burning flags".

Another protester, Mustafa, whose father left Gaza in 1976, was at the rally with his three children.

"We are not against Jewish people , they have been in Palestine for a long time side by side with the Muslims and the Christians, we are all Palestinians. We are against the Zionists" he said.

Organisers said they planned to march through central Sydney next weekend.

The Executive Council of Australian Jewry was not immediately available for comment on Sunday's rallies.

Countries across the developed world are curbing pro-Palestinian protests out of concern the Israel-Hamas conflict could trigger violence at home. France banned pro-Palestinian protests on Thursday saying they were likely to "generate disturbances to public order".

In Sydney, police arrested three men on Friday outside the Jewish Museum of Australia in Sydney for making Nazi salutes, media reported. Australia's intelligence chief has called for people to tone down rhetoric that could inflame tensions.

(Reporting by Sam McKeith and Lewis Jackson in Sydney; Editing by Muralikumar Anantharaman)