Hamdan insisted that Israel "started the war."
"We are defending ourselves," he said, arguing that Netanyahu was looking to cement support in advance of an election in two months.
Israeli Defense Minister Ehud Barak denied that any politics are involved in the decision.
Speaking to CNN, Barak said Israel has destroyed most of the "heavy long-range rockets" used by militants in Gaza and is working to "systematically destroy" installations in which other rockets are produced.
"It will take some time," he said.
Israeli forces are going after Hamas weapons, storage bunkers, weapons labs and workshops, an Israeli official told CNN. The official has direct knowledge of Israeli plans but declined to be identified because of the sensitive nature of the information.
The Israeli army moved nearly a division's worth of troops -- perhaps 1,500 to 2,000 -- to the border, the official said.
While multiple militant groups are behind the rocket attacks, Israel holds Hamas responsible ever since it took control of Gaza, Barak said.
Hamas' military wing has claimed responsibility for numerous operations in the past. The U.S. government and the European Union consider Hamas a terrorist organization.
Netanyahu issued a statement Thursday saying, "In recent days and weeks, Hamas and the other terrorist organizations in Gaza have made normal life impossible for over 1 million Israelis. No government would tolerate a situation where nearly a fifth of its people live under a constant barrage of rockets and missile fire."
He added, "The terrorists are committing a double war crime. They fire at Israeli civilians, and they hide behind Palestinian civilians. And by contrast, Israel takes every measure to avoid civilian casualties."
Ghazi Hamad, Hamas' deputy foreign minister, told CNN that Hamas was sending rockets toward Israel's population because Israel thinks "that it is easy to kill people in Gaza," enter the area and "do everything" it wants in Gaza. "We send a message to them that Gaza is not an easy bone. ... You can't eat Gaza in one minute. If you do something, we will react."
Palestinian lawmaker Mustafa Barghouti said the Israeli government has "proven that it is a government of war and not peace."
Israel is "the oppressor," not the victim, he said.
Concern over possibility of a ground assault
The sudden increase in violence has raised fears of a widening conflict that could lead to an Israeli ground assault.
Tony Blair, envoy for the Middle East Quartet, which is working to bring about a peace agreement, said on Thursday: "I don't think we should be of any doubt at all that if this situation continues and it escalates, it's going to be really serious and tragic -- not just for Israelis and Palestinians, but actually it will cause a huge amount of upheaval right across the region, and this is a region, as you know, that doesn't require more upheaval right now."
British Foreign Secretary William Hague issued a statement saying he is "gravely concerned" and calling on all sides to avoid civilian casualties.
"Hamas bears principal responsibility for the current crisis. I utterly condemn rocket attacks from Gaza into southern Israel by Hamas and other armed groups. This creates an intolerable situation for Israeli civilians in southern Israel, who have the right to live without fear of attack from Gaza. The rocket attacks also risk worsening the plight of Palestinian civilians in Gaza, which is already precarious."
Palestinian President Mahmoud Abbas, who leads the Palestinian Fatah movement based in the West Bank, is cutting short a visit to Europe to follow developments of "the Israeli aggression on the Gaza strip," PLO Executive Committee member Saeb Erakat said.