While no-one was injured in the latest clash, weapons including nulla-nullas, spears, a baseball bat and a machete were seized by police.
Acting Southern Commander Drew Slape said the “reprehensible behaviour” had no place in the community.
“Our dedicated officers have responded to calls to assist and we will have extra members working tonight, giving up their time off in order to keep Alice Springs residents safe,” he said.
It is unknown if the disturbance will extend the curfew.
Police Minister Brent Potter said the decision to extend the curfew would be made on Thursday morning after he and Northern Territory Police Commissioner Michael Murphy had reviewed the “most up-to-date” information.
“The police commissioner and I are in regular contact regarding the on-going curfew in Alice Springs,” Potter said.
Murphy on Monday declared a 72-hour curfew which banned adults and children from entering the town centre from 10pm to 6am each night, unless they have a valid reason to be there.
Under controversial laws passed on urgency in May, the police commissioner can call a snap curfew but only the Police Minister can extend it upon the commissioner’s request.
Murphy said he made the decision to lock down Alice Springs after a string of “violent incidents” at the weekend.
Northern Territory police confirmed about 5000 people travelled to Alice Springs in recent weeks for school holidays, the Alice Springs Show and NAIDOC (National Aboriginal and Islander Day Observance Committee) week.