It said the drone, which was shot down in early April, was still in Malian territory, which would make the incident a violation of its airspace.
Algeria has rejected the accusation, citing defence ministry radar data to argue that the reconnaissance drone from junta-led Mali had violated its own airspace.
The issue has sparked a diplomatic crisis that has seen the neighbours recall their ambassadors and close airspace to each other.
In a statement Thursday, Mali's territorial administration ministry said it had "submitted an application instituting proceedings against Algeria before the International Court of Justice".
The destruction of the drone within Malian territory "constitutes not only an aggression, a hostile act, but also a blatant violation of the principle of non-use of force and an act of aggression", it argued.
"This flagrant aggression is the culmination of a series of hostile acts and clearly demonstrates an unhealthy collusion between terrorists and the Algerian regime," it added.
Relations between Mali and its northern neighbour have deteriorated in recent years.
Mali accuses Algeria of maintaining "proximity to terrorist groups", particularly in the border region.
In January 2024, Mali's junta scrapped a 2015 peace deal with separatist groups brokered by Algeria and which had long been considered essential for stabilising the country.
Since 2012, Mali has been gripped by violence from jihadist groups linked to Al-Qaeda and the Islamic State group as well as local criminal gangs.