Amnesty International has accused Hezbollah of acts amounting to war crimes in the conflict with Israel.
Amnesty said the rocket attacks were deliberate and indiscriminate
It says the Lebanese militant group deliberately targeted civilians with rockets in the 34-day war - a "serious violation of humanitarian law".
Amnesty has already accused Israel of committing war crimes by targeting Lebanon's civilian infrastructure and is urging a UN inquiry into violations.
Hezbollah rejected the report, calling it a result of US and Israeli pressure.
Hezbollah MP Hassan Fadlallah said Amnesty should analyse the number of civilians killed on each side, before accusing Hezbollah of war crimes.
Amnesty says what it calls Israel's violations can in no way justify Hezbollah's actions.
The latest Amnesty report said: "Hezbollah's rocket attacks on northern Israel amounted to deliberate attacks on civilians and civilian objects, as well as indiscriminate attacks, both war crimes under international law."
It said Hezbollah had fired nearly 4,000 rockets into northern Israel, killing 43 civilians and forcing hundreds of thousands to flee.
It noted that although Hezbollah had said its policy was not to target civilians, its leader Sheikh Hassan Nasrallah said the policy was changed in reprisal for Israeli attacks on Lebanese civilian areas.
Amnesty said Sheikh Nasrallah did a U-turn on civilian targeting
It quoted Sheikh Nasrallah as saying: "As long as the enemy undertakes its aggression without limits or red lines, we will also respond without limits or red lines."
Amnesty International's Secretary General, Irene Khan, said: "Civilians must not be made to pay the price for unlawful conduct on either side."
Amnesty repeated its call for "a comprehensive, independent and impartial inquiry" by the UN into the violations and to ensure there was "full reparation" to victims.
It said those responsible for civilian suffering were "escaping all accountability".
Ms Khan said: "Justice is urgently needed if respect for the rules of war is ever to be taken seriously."
Amnesty's report on 23 August said Israel had targeted homes, bridges, roads and water and fuel plants as an "integral part" of its strategy.
It said Israeli claims of "collateral damage" were "simply not credible".
Israeli government spokesman Mark Regev said Israel's actions during the war were "in accordance with recognised norms of behaviour during conflicts and with relevant international law".
Amnesty says it will publish further reports about other aspects of the war, including attacks by Israeli forces that resulted in heavy civilian casualties and charges that Hezbollah used Lebanese civilians as a cover for their operations.
About 1,000 Lebanese, mainly civilians, died in the fighting, while 161 Israelis, mainly soldiers, were killed.
Israel launched its offensive after Hezbollah militants seized two of its soldiers and killed several others during a cross-border raid on 12 July.