Footage of six boys being gassed at the Don Dale detention centre in 2014 has led to widespread condemnation of conditions for youth detainees.
All six are seeking damages for mistreatment, the Australian Broadcast Corp (ABC) reports.
The NT government had initially said it would bring a counter suit.
According to the ABC report, authorities say serious damage, costing A$89,000 ($67,000;£51,000), was caused when the boys escaped from the centre in 2015.
One day later, they allegedly stole a car and rammed it into a garage door at the centre, causing another A$74,000 worth of damage.
The boys' lawyer has argued his clients would not have tried to escape were it not for the "poor and restrictive conditions" in which they were held.
Footage of the tear gas incident and repeated mistreatment of a boy named Dylan Voller prompted Prime Minister Malcolm Turnbull to order a top-level government inquiry into youth detention in the state.
In one incident, Voller was cuffed to a restraint chair while wearing a hood and left alone for over an hour.
Youth detention rates are three times higher in the NT than elsewhere in Australia, according to the Australian Institute of Health and Welfare.
Although the institute doesn't break down Indigenous youth incarceration rates specifically for the NT, young Indigenous people across Australia are 26 times more likely to be in detention than non-Indigenous youth.
The government of Australia's Northern Territory (NT) is dropping legal action against two boys who were subdued with tear gas at a detention centre.