Howard was speaking for the first time since fighting in the southern suburb of Cronulla left 31 people injured and saw 16 arrests.
Police have formed a strike force to track down the instigators of the running battles that involved drunken mobs of white men yelling racial slurs, young men of Arab descent and hundreds of police officers.
One officer was admitted to hospital after being stabbed in the back.
"Attacking people on the basis of their race, their appearance, their ethnicity, is totally unacceptable and should be repudiated by all Australians irrespective of their own background and their politics," Howard said.
"But I'm not going to put a general tag [of] racism on the Australian community," he said. "I do not accept that there is underlying racism in this country."
New South Wales state premier, Morris Iemma, said police would hunt down the instigators of the violence, which the authorities said was fanned by neo-Nazis.
"Let's be very clear, the police will be unrelenting in their fight against these thugs and hooligans," Iemma said.
31 people were injured in the riots
(Picture: Sky News)
The rioting began on Sunday after thousands of drunken white youths descended on Cronulla beach in southern Sydney. It follows an assault last week on two lifeguards by youths, reportedly of Middle Eastern origin.
Fighting spread to neighbouring suburbs with retaliatory attacks by groups of Arab-looking youths.
The violence has shocked Australia's normally peaceful, largest city of 4 million. Sydneysiders like to boast of their home as a cultural melting pot, with ethnic communities from all over the world.
Local paper, the Daily Telegraph, summed up the shock. Its headline declaring simply "Our disgrace" over a picture of white youths attacking a man of Arab appearance on a train.
Scale of unrest
Locals 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 often visited by many youngsters of Middle Eastern ethnicity from the poorer suburbs of western and southern Sydney.
Some experts believe that a general trend of anti-Muslim resentment, that has risen since the 9/11 attacks in the United States and the 2002 Bali bombings in Indonesia that killed 88 Australians, may have been a factor in Sunday's riots.
Local residents say anti-Muslim
sentiment had been on the rise
Government lawmaker Bruce Baird said many Cronulla locals were angry, particularly after six women from the suburb were killed in the Bali bombings.
"Where this riot took place is actually the site of where we've got the Bali memorial for these women," Baird told ABC radio.
Local leaders are now appealing for calm and urging against retaliatory attacks.
Plea for calm
Kuranda Seyit, director of a group called the Forum on Australia's Islamic Relations, criticised all those involved in the rioting.
"Australia is a pluralist society, with many faiths and traditions all ravelled into one," he said.
"This is the unique success of this nation and we cannot let it fall into chaos and lawlessness," he added.
"I realise that the initial behaviour by the thugs who beat the lifeguard was unacceptable but to take it out on anyone who the mob think are not one of them, is not the solution."