Qaani told Haniyeh that Iran "stands alongside the nation of Palestine" and condemned Israel for acting "against all international laws and conventions," IRNA reported.
On Sunday, the Israeli military announced that it targeted the home of a top Hamas leader in Gaza.
Since fighting broke out earlier last week, Hamas and the Islamic Jihad group have acknowledged that 20 fighters have been killed in targeted Israeli strikes, while the Israeli military has said that this number is significantly higher.
US Secretary for Israel-Palestinian Affairs Hady Amr was to hold talks Sunday with Israeli leaders before meeting Palestinian officials to seek a "sustainable calm," the State Department said.
At least 132 people have been killed in Gaza since Monday, including 32 children and 21 women, and 950 others wounded, Palestinian medical officials said
In renewed airstrikes on Gaza, Israeli warplanes struck a six-story residential building that it said belonged to Hamas, the Islamist group that controls the Palestinian enclave. Netanyahu said Israel has struck close to a thousand militant targets in Gaza in total.
The four days of cross-border violence showed no sign of abating and Israeli Prime Minister Benjamin Netanyahu said the campaign "will take more time".
The Palestinian militant group Hamas has confirmed on Wednesday that several of its top commanding officers were killed in Israeli strikes, including the military chief of Gaza city.
Israeli forces announced that they killed 16 Hamas fighters, including a senior commander and numerous weapons developers, in an airstrike on a Hamas command post in the Gaza Strip.
According to the Palestinian Ministry of Health, at least 21 civilians have been killed by Israeli air raids on the besieged Gaza Strip, after Hamas launched retaliatory rockets from the coastal territory.
The aerial bombardment occurred after Hamas fired several rockets at Israel, after Israel refused to withdraw forces from the Al Aqsa Mosque in Jerusalem.
Israel has blocked 1000 doses of the Russian-made Sputnik V coronavirus vaccine, intended for frontline medical workers and key personnel in the tumultuous Gaza Strip.
The Gaza Strip has yet to any vaccines, with over 53,000 cases and 537 deaths since the start of the pandemic, and limited support in the management of this public health crisis.
In late December, Hamas and Islamic Jihad staged joint military exercises in the coastal territory, during which they fired rockets out to sea, in the first exercise of its kind.