The NT Chief Minister's office says the Government has withdrawn counter-claims made against two detainees who were tear-gassed in the Don Dale Youth Detention Centre.

But Adam Giles has decided not to settle with the six detainees who are suing the Government, saying they will defend the lawsuit being brought by them.

Mr Giles, who took over the Corrections portfolio after footage of mistreatment of youths in detention air on Four Corners, decided there should be no settlement.

The Chief Minister was advised the settlement cost could be up to $250,000 for each plaintiff, the spokesperson said.

"I'm standing up for Territorians. I don't believe taxpayer money should be going towards windfall payouts to prisoners," Mr Giles said.

Philippa Martin, from the North Australian Aboriginal Justice Agency, who are representing the two young men, said she had not been formally advised that the counter-claim had been dropped, but said she welcomed reports from the media.

The six young men all lodged civil suits before Four Corners went to air, and the Government's counter-claim was also lodged before the program screened.

The Government had lodged a counter-claim on July 4, seeking compensation for damage it said two boys did during a breakout in May 2015.

The Government said the pair participated in a riot which caused $89,000 in damage.

They then returned to Don Dale in a stolen car, ramming their way through a roller door and doing burnouts in the grounds, causing $74,000 in damage.

The Government also filed a further claim against one of the boys for a breakout attempt on February 24, 2015, which the Government said cost $45,000.

But the Government announced it had dropped its counter claim, six hours after the ABC first reported it was suing the boys.

The Chief Minister's office said it will continue to defend the civil claims, which are seeking exemplary damages from the Government over the tear-gassing and a string of other allegations.