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.

Israel says it has called thousands of residents in Gaza to warn them of strikes and dropped leaflets in Gaza warning Palestinian civilians to "avoid being present in the vicinity of Hamas operatives," the IDF said.

It also uses "roof knocking" -- targeting a building "with a loud but nonlethal bomb that warns civilians that they are in the vicinity of a weapons cache or other target. This method is used to allow all residents to leave the area before the IDF targets the site with live ammunition."

Roar of planes followed by 'kaboom'

At one point Thursday morning, 13 rockets were fired in quick succession from Gaza into Israel. A CNN crew could see trails of smoke as they reported from the Israeli side of the Erez Crossing on Gaza's northern border.

The crew was forced to take cover after rockets struck near the border crossing.

Later, reporting from Gaza City, the crew witnessed airstrikes and plumes of black smoke in many parts of the city.

Egypt watches with interest

The escalating violence is likely to further erode Israel's fragile relationship with Egypt, which recalled its ambassador to Israel on Wednesday in protest over the ongoing strikes. It also delivered a formal protest to the Israeli government.

On Thursday, when asked by CNN's Hala Gorani if treaties between Egypt and Israel are in danger, the chief of the Egyptian presidential cabinet said no.

"Not at all. Because we have declared several times, repeatedly, that we abide by our international commitments," Mohamed Refa'a al-Tahtawi said. "But respecting a peace treaty does not mean to stay idle or indifferent to what is going on along our borders.