At least four militants have been killed and several other people injured in Israeli air strikes in Gaza.
The Israeli military said it targeted those behind the firing of more than 70 rockets into southern Israel since midnight, injuring five people.
Schools have closed on both sides of the border for fear of more attacks.
The violence comes as the EU's foreign policy chief, Catherine Ashton, visits the region to try to revive the stalled Middle East peace process.
She was scheduled to meet Israeli President Shimon Peres and Prime Minister Benjamin Netanyahu. Her talks with Defence Minister Ehud Barak were cancelled on Wednesday so he could tour the border with Gaza.
On Thursday, Baroness Ashton will meet Palestinian Authority President Mahmoud Abbas and his Prime Minister, Salam Fayyad.
"This is a critical time for the wider Middle East," she said.
Hamas, which governs Gaza, is not even part of the peace process, which has seen little US engagement since direct negotiations collapsed two years ago, reports the BBC's Jon Donnison in Gaza City.
Our correspondent says the thud of explosions across Gaza and parts of southern Israel at dawn on Wednesday were a reminder that the conflict has not gone away.
Hamas's military wing, the Izz al-Din Qassam Brigades, said it had been involved in firing dozens of rockets and mortars into Israel.
Six rockets were fired on Tuesday evening before the Israel Defence Forces (IDF) launched its first air strike, targeting a launch squad in northern Gaza.
Two further rocket launch attempts were "thwarted" overnight by further Israeli Air Force strikes, the IDF said, confirming "hits".
Palestinian officials said three members of the Izz al-Din Qassam Brigades were killed.
Then at 07:00 (05:00 GMT), a barrage of 40 rockets was fired into southern Israel, the IDF said. Two foreign farm workers and an IDF officer were critically wounded and evacuated by helicopter to a nearby hospital, it added. Two other people suffered light injuries.
Another 25 rockets were fired over the next two hours, seven of which were intercepted by Israel's Iron Dome missile defence system. A total of 74 missiles hit Israel over a period of 24 hours, the IDF said.
In response, Israeli aircraft and tanks targeted another rocket launching site in northern Gaza, killing another militant, Palestinians said.
Prime Minister Netanyahu promised to continue "targeted attacks" on militants launching rockets into Israel.
"We didn't ask for this escalation and didn't initiate it," he said. "But if it continues, we are prepared to embark on a far more extensive and penetrating operation."
Asked if he was considering a ground operation, Defence Minister Ehud Barak told Israel Radio: "Nobody is eager for this but we will act, as we are required to stop this wave and to increase the effectiveness of the operation."
In a statement, the Izz al-Din Qassam Brigades and a smaller Gaza-based militant group, the Popular Resistance Committees (PRC), said: "These holy missions come in response to the repeated, continuous crimes of the enemy against our people."
Two members of the groups were killed in an Israeli air strike on Monday. The Israeli military said it had targeted the militants after they fired mortars at a ground patrol. Palestinian sources said the patrol had entered Gaza near Beit Hanoun.
On Tuesday morning, an Israeli soldier was critically injured after a bomb exploded as he patrolled near the Gaza border fence. The armed wing of the leftist Popular Front for the Liberation of Palestine (PFLP) said it was behind the attack.