The Sydney authorities are warning of more racial unrest over the weekend, as text messages encouraging violence continue to circulate in the area.
Police are keeping an especially close watch on Cronulla beach
"We expect further problems," New South Wales Police Minister Carl Scully told reporters on Wednesday.
After two nights of violence, Tuesday night was mainly calm as hundreds of police patrolled the troubled areas.
Arab community leaders have called for a curfew on Friday and Saturday nights, and all of Sunday, to stop any trouble.
Ahmad Kamaledine, president of the Lebanese Moslems Association, said: "Those who violate the curfew will be doing so in defiance of their faith, of the [holy] law, and their community leaders", according to Australian media reports.
He was speaking after a number of meetings were held across Sydney aimed at defusing the violence.
Representatives of Middle Eastern and surfing groups met at Cronulla - the scene of most of the violence - and said they were sending out text messages telling people to stop the violence.
New South Wales state Premier Morris Iemma said police would keep a close watch on places of worship in the coming days.
He was speaking as authorities investigated whether a fire at a Protestant church hall in another Sydney suburb could be linked to the violence.
Four men were reportedly seen outside the church, in a largely Middle Eastern neighbourhood, shortly before the blaze started in the early hours of Wednesday morning.
"I've been in contact with the police this morning and the police are treating it as suspicious," Mr Iemma said.
The large-scale violence in Sydney started on Sunday, when thousands of young white men attacked people of Arabic and Mediterranean background on Cronulla Beach - apparently in revenge for a recent attack on two lifeguards.
Many of the rioters had been alerted to congregate in the area by receiving mobile text messages.
The fighting then spread to other parts of the city, injuring more than 30 people, including police officers.
The violence continued on Monday night, apparently in retaliation, despite calls for calm and ethnic tolerance by Prime Minister John Howard and other senior figures.
Mr Howard told reporters covering an East Asia Summit he attended in Kuala Lumpur on Wednesday: "Incidents like this... can happen in any country."
Text messages that fuelled the riots have now started circulating in two other states - Victoria and Queensland - police have said.