Shadow Indigenous affairs spokesperson Jacinta Nampijinpa Price says Mparntwe/Alice Springs would "welcome" another curfew, even if it was only temporary.
It comes as the NT government flagged the possibility of another curfew for the second time this year, after four off-duty police officers were allegedly assaulted on Sunday morning.
Speaking on ABC radio on Monday morning, Senator Price, who was a strong advocate for the previous curfew in March, said while the town would likely welcome another curfew, there were "underlying issues taking place".
"Indigenous children [in] my community and throughout the Northern Territory experience the highest rates of domestic and family violence [and] child sexual abuse," Ms Price said.
"It's no wonder that we have circumstances [where] these children come out of dysfunction where we're seeing again, another rise in violent crime in the community."
The Warlpiri/Celtic Senator has advocated for a royal commission into child sex abuse in remote communities, which was criticised by over 50 child safety organisations and experts.
Ms Price has also gone against the grain of the majority of Indigenous groups in the country by explicitly rejecting calls for self-determination as a means to close the gap.
Police Minister Brent Potter flagged the idea of a curfew on Sunday, stating: "[Police Commissioner Murphy has] told me he is looking at the curfew. It is a power that he has within his means … He'll make that deduction, that's up to him, and I'm likely to hear back from him later."
On Monday morning, President of the NT Police Association, Nathan Finn, said the commissioner had yet to decide on measures and at this stage, the union wasn't expecting a curfew to be announced.
"I have spoken to the commissioner this morning, he's relayed his concerns of obviously what's occurred in Alice Springs in the last 72 hours," Finn said.
"He's in consultation with his command team to make that determination whether the curfew is required.
He said a lot of considerations needed to be looked at, including "whether we've got enough resources to actually police this curfew".
During the previous curfew, South Australian police had to be drafted in to alleviate NT Police, many of whom were based outside of Alice Springs.
"It's sad we're talking about this only three months prior to the previous one made in Alice Springs," Finn said.
"It's a tough decision to make but a decision that needs to be made by the commissioner and local command team in respect to obviously placing that curfew in.
"We need those resources, though, to make sure we can police the curfew if that's the decision that's made."
In May, the NT government introduced new legislation to enable the easier implementation of curfews, describing it as a "common sense plan to reduce crime and anti-social behaviour".
The government said the new laws will be administered by the police, who recently received record funding in the NT budget, and any extension will need to be signed off by the Police Minister.
