Spokesman Lamine al-Hachemi said another child was seriously wounded and the parents of the dead children were also injured in the air strike that hit their home in Al-Fernaj, a suburb southeast of Tripoli.
Five other civilians were wounded in the attack.
Libya's UN-recognised Government of National Accord (GNA) accused forces of strongman Khalifa Haftar of launching the "criminal" air strike.
"This criminal act carried out by the aircraft of the war criminal (Haftar), is the latest in a series of attacks that have targeted airports, public and private buildings and... terrorised civilians," it said on Facebook.
The UN mission in Libya UNSMIL condemned "the reckless disregard for the lives of innocent people".
"Once again, innocent children pay the ultimate price," said a statement, adding that the air strike "was reportedly conducted by a fighter jet belonging to (Haftar's) 'LNA' forces" .
UNSMIL "will not stand idly by and watch war crimes being committed, and innocent lives being lost, almost every day," it added.
Ahmad al-Mismari, spokesman for pro-Haftar forces who control eastern Libya, said an air strike was carried out against "a camp of the intelligence services in Al-Fernaj" but he denied that a house or civilians were targeted.
Haftar launched an offensive to capture Tripoli, seat of the GNA, in April but since then frontlines have barely shifted.
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