The court said although Russian authorities had information that an attack was being planned on a school in North Ossetia, they failed to do enough to disrupt the plot and had not sufficiently protected the hostages.
Russia reacted furiously to the judgement, saying it was "absolutely unacceptable".
The school was stormed on September 1, 2004 by militants demanding the withdrawal of Russian troops from the war-torn republic of Chechnya.
After three days of fruitless negotiations, explosions in the school prompted Russian security forces to storm the gymnasium.
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A total of 184 children were among the 334 dead as the siege came to a bloody end.
Russian authorities argue they took the best course of action faced with armed extremists, but many of the survivors and their relatives believe the security services were to blame for the firefight.
The case was brought to the Strasbourg-based court by more than 400 Russians either involved in the incident or whose relatives were taken hostage or killed.
"Nevertheless, not enough had been done to disrupt the terrorists meeting and preparing."
The judges found that "insufficient steps had been taken to prevent (the attackers) travelling on the day of the attack; security at the school had not been increased; and neither the school nor the public had been warned of the threat".
Kremlin spokesman Dmitry Peskov said Russia found it "impossible" to agree with the wording of the judgement.
"Such phrasing for a country that has suffered an attack is absolutely unacceptable," he told journalists.
There was an additional violation in the use of "lethal force by security forces".
"In the absence of proper legal rules, powerful weapons such as tank cannon grenade launchers and flame-throwers had been used on the school," which had contributed to the casualties among the hostage, the court said.
The judges also said there were "serious shortcomings" in the investigation into the attack, especially that there had been "no proper examination of how the victims had died".
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