A police spokesman said the rampage broke out in Cronulla, the same beach-side suburb where a night of race riots resulted in scores of arrests on Sunday, and in neighboring Caringbah.
"We have shops damaged at Caringbah, cars damaged at Cronulla," said Paul Bugden, spokesman for New South Wales police. "We have six arrests at this stage."
One person was apparently hit with a rock outside the Cronulla police station, he added, saying that youths riding around in cars were involved in the violence.
The Australian Associated Press news agency said gunshots were heard near Cronulla beach, but police could not confirm the report.
Bugden said he did not have descriptions of those involved in Monday night's violence, but said the rampage, which spilled over into the early hours of Tuesday morning, "obviously stems from the last 24-48 hours."
By around 12:30 a.m. Tuesday, calm had returned to the suburbs targeted by the carloads of youths.
A resident of the suburb of Brighton-Le-Sands, Steven Dawson, said a bottle thrown through his apartment window showered his 5-month-old son with glass, but did not hurt the child.
"That bottle could have killed him," Dawson said.
Horst Dreizner said a car was rammed through the front doors of his denture store, causing thousands of dollars worth of damage.
He said he feared the violence would escalate.
"Personally, I think it is only the beginning," he said in a telephone interview.
Australian Associated Press, citing a resident who declined to be named, said men riding in up to 50 cars and wielding baseball bats converged on Cronulla, smashing cars. Ambulances were called to help at least one injured man seen lying on the side of the road.
Earlier Monday, Prime Minister John Howard condemned , but said he does not believe Australian society has an undercurrent of racism.
"I do not accept that there is underlying racism in this country," he said.
Sunday's fighting left 31 people injured, including police and paramedics. One was hospitalized after being stabbed in the back by a man police said was Arab in appearance. There were 16 arrests.
"What we have seen yesterday is something I thought I would never see in Australia and perhaps we have not seen in Australia in any of our life times, and that is a mass call to violence based on race," Community Relations Commission chairman Stepan Kerkyasharian told Sky News.
New South Wales state police chief Ken Moroney called Sunday's rioting among "the worst violence that I have ever seen in my policing service of 40 years."
The state's political leader, Morris Iemma, said police would hunt down the instigators of the violence, which authorities said was fanned by neo-Nazis.
"There appears to be an element of white supremacists and they really have no place in mainstream Australian society," Police Minister Carl Scully said. "Those sort of characters belong in Berlin (in the) 1930s."
The violence shocked Sydney, a city of 4 million that prides itself on being a largely harmonious cultural melting pot.
One government lawmaker, Bruce Baird, said anti-Muslim resentment that has risen since the Sept. 11, 2001, attacks in the United States and the 2002 Bali bombings in Indonesia that killed 88 Australians also played a role.
Local residents say there have been frequent minor racially charged confrontations on Cronulla beach, but never anything close to the scale of Sunday's unrest.
Cronulla is easily accessible by train and often is visited by youngsters, many of Middle Eastern ethnicity, from the poorer suburbs of western and southern Sydney.
Residents accuse the visitors of traveling in gangs, being disrespectful and sometimes intimidating other beach-goers. That escalated when two men believed to be of Arab descent attacked two volunteer lifeguards last week, sparking a flurry of mobile phone text messages calling for retaliation.