"We strongly condemn the shelling of a school in the Ain Zara area and consider it to be another war crime against civilians", the GNA Presidential Council said in a statement, released on Twitter.
According to local media reports, no one was injured in the airstrike, but the administration of the school had to relocate refugees, hosted at the school.
The forces loyal to the GNA have announced a counteroffensive, dubbed Volcano of Rage, to repel LNA.
Libya has been suffering from unrest since 2011, when its long-time leader Muammar Gaddafi was overthrown and killed. Since then the country has been divided between two rival governments, with an elected parliament governing the country's east and the UN- and EU-backed GNA ruling the west from Tripoli.