"We will defeat it, God willing," he said.
Israeli jets have carried out more than 30 air raids on Monday.
The Israeli military said it hit a mosque in the northern town of Jabaliya "where arms were being stored, as well as houses containing arms caches and vehicles that were transporting rocket launchers and armed men".
"We have hit Hamas hard, but we have not yet reached all the goals that we have set for ourselves," Ehud Barak, the Israeli defence minister, told members of parliament.
"Gaza City is partially surrounded," he said.
Al-Zahar warned that Israel's war on Gaza had opened it up to retribution by Palestinian fighters.
"They have legitimised the murder of their own children by killing the children of Palestine," he said.
"They have legitimised the destruction of their synagogues and their schools by hitting our mosques and our schools."
Palestinian fighters have continued to fire rockets into southern Israel despite the Israeli military operation.
But Major Avital Leibovitch, an Israeli military spokeswoman, told Al Jazeera that the cross-border attacks were being slowed.
"Those rockets are coming less and less, because today we have had approximately 20 launchings which is one-tenth of Hamas's original launching capabilities ... there are sign that Hamas is weakening," she said.
"The second stage of the operation is going as planned, we have a variety of forces joining in this and it is proceeding according to the plan."
Al Jazeera's Ayman Mohyeldin, reporting from Gaza City, said that the Palestinian armed groups had certainly been weakened by the military operation.
"There is no doubt that they have sustained casualties ... but they are still very much operational," he said.
"They are engaged in hit-and-run type of tactics and have been preparing for this for several months by laying explosive devices and booby traps."
Abu Obeida, the spokesman for Hamas's Izz-e-din Al-Qassam Brigades, warned the Israeli military that it had many fighters ready to face it in the Gaza Strip.
"We have prepared thousands of brave fighters who are waiting for you in each corner of the street and will welcome you with fire and iron," he said.
"As long as the aggression intensifies, your losses will increase and you will sink further into the Gaza quagmire."
At least one Israeli soldier has been killed in fighting since the ground offensive was launched on Saturday, while dozens of Palestinians, including many civilians have died.