Opposition Leader Tony Abbott won't demand the reinstatement of the Northern Territory's banned drinkers register, despite being concerned about his territory colleagues' decision to scrap it.

Prime Minister Julia Gillard has written to the NT's Country Liberal Party (CLP) government urging them to reinstate the register, fearing the "rivers of grog" are beginning to flow again.

In his response to Ms Gillard's Closing the Gap address, Mr Abbott told parliament he shared the prime minister's concerns about the register.

However, speaking to reporters in Queanbeyan on Thursday, he ruled out demanding the CLP overturn its decision.

"I'm not in the business of being dictatorial or prescriptive," he said.

"I'd be happy to hear from the territory what they think they can do which is more effective than the banned drinkers register, because what I'm interested in is not argy bargy between different levels of government.

"What I'm interested in is getting a better outcome on the ground."