A million Israelis are in range of the rockets. Israeli leaders have warned they won't tolerate continued barrages and have threatened a more forceful response.
Six Palestinians have been killed in Israeli counterstrikes, Palestinians said.
Israeli Prime Minister Benjamin Netanyahu told foreign ambassadors that Israel would defend itself. He spoke during a visit to Ashkelon, a southern city that has been battered by Gaza rockets.
"I don't know of any of your governments who could accept such a thing. I don't know of any of the citizens of your cities, who could find that acceptable and something that could proceed on a normal basis. I think the whole world understands that this is not acceptable," Netanyahu said, referring to the rocket attacks.
"We'll take whatever action is necessary to put a stop to this. This is not merely our right, it's also our duty," he said.
Israeli Defense Minister Ehud Barak met with the military chief of staff and other senior officials Monday evening to determine how to respond to the rocket fire.
Some Israelis are demanding a military operation similar to Israel's bruising incursion into Gaza four years ago. Others believe Israel should target Hamas leaders, a method it used to kill dozens of top militants nearly a decade ago.
Palestinian health official Ashraf al-Kidra said six Palestinians, including two members of the Islamic Jihad, have been killed and dozens injured in Israeli strikes since the latest fighting began over the weekend. The Israeli military said it struck rocket launcher squads and a weapons warehouse.
More than 110 rockets have hit Israeli towns since the latest round began, the military said.
At least a dozen rockets slammed into Israel Monday. One rocket hit a house, and another smashed into a factory on Monday, the military said. Three civilians were injured by shrapnel and dozens were treated for shock when rockets exploded in residential areas, Israel's emergency rescue services said.
The latest round of violence began when Gaza militants fired an anti-tank missile at an Israeli jeep patrolling on the Israeli side of the border on Saturday, wounding four soldiers.
An Egyptian official said that efforts are under way to try to achieve a truce. He was speaking on condition of anonymity because he was not authorized to brief reporters.