The Northern Territory Government has rejected the Prime Minister's call to reinstate a policy that banned problem drinkers from buying takeaway alcohol.

The Territory's former Labor government introduced the Banned Drinker Register (BDR) in 2011 but the Country Liberals dismantled it when they came to power last year.

Julia Gillard has told Parliament that alcohol-related violence and hospital admissions have risen because problem drinkers now have greater access to alcohol.

But the Territory's Acting Chief Minister Robyn Lambley says the Banned Drinker Register was ineffective.

"We have been appointed with a clear majority ... on the basis that we would scrap the BDR," she said.

"We did that for one reason and one reason only: It wasn't working.

"We do not intend to reinstate the Banned Drinker Register.

"To think that the Banned Drinker Register was tight enough to stop people on the register from drinking is a furphy," Mrs Lambley said.

She derided the scheme as "an absolute nonsense".

"These people are very cunning, they're addicted and they will find a way to access alcohol."

She cited the case of one man who, despite being listed on the BDR, was placed in protective custody 117 times.

Federal Indigenous Affairs Minister Jenny Macklin says effective alcohol restrictions must continue.

"There were, we understand, five alcohol-related deaths in Alice Springs over the Christmas period," she said.

"The evidence is serious and the evidence also is that the Banned Drinkers Register helped.

"It helped make sure that people who had trouble with alcohol were not able to get access to it as easily."

Federal Indigenous Health Minister Warren Snowdon described the Territory Government's attitude to the BDR as "irresponsible, inappropriate and bad".

In Alice Springs, Dr John Boffa from the People's Alcohol Action Coalition has backed the Prime Minister's call to reinstate the BDR immediately.

"Removing the register was a travesty," he said.

"This was one strategy that was working.

"We have got the highest alcohol-related harm in Australia and it is not acceptable to not implement all possible measures that we know are having an effect."

Territory Opposition Leader Delia Lawrie says it is clear the banned drinker register should never have been scrapped.

"The Prime Minister and Tony Abbott are joining the police, the nurses, the doctors, the health practitioners around the Territory saying the Banned Drinker Register should be in place," she said.

"It is time for Terry Mills to admit he has got it wrong."