At least 21 Qassam rockets and eight mortar shells were fired at southern Israel by mid-morning, with the location of 10 pinpointed. One of the mortars struck a direct hit on a house in Kibbutz Sha'ar Hanegev, causing extensive damage.
Most of the Qassams and shells were fired overnight, while three rockets hit Netivot and another two Grad-type missiles exploded in a public area of Ashkelon after sunrise.
The political-security cabinet held an urgent session on Wednesday morning to discuss ways of responding to the fire, calling in Defense Minister Ehud Barak for consultations.
The defense establishment ordered border crossings to Gaza to remain closed on Wednesday in response to the attacks. On Tuesday, Israel had said it would to open the border to allow food and medicine to enter the Gaza Strip, after days in which the crossings have been closed due to the ongoing rocket fire from Gaza.
The shipment of humanitarian aid was to include five trucks from Egypt, which requested that Israel open the Kerem Shalom crossing to let the convoy pass, and 30 from the West Bank containing goods supplied by international organizations.
Rescue services have raised their alert to the second highest level and the Home Front Command has warned Gaza-area residents to keep children indoors as the barrage continues.
The barrage came after a senior Hamas official said in an interview published Tuesday that the Islamist group would be willing to renew its cease-fire with Israel without adding any new conditions.
The barrage was apparently launched in response to the Israel Defense Forces' killing of three armed Palestinians, who were seen laying bombs along the Israel-Gaza border on Tuesday.
Six rockets struck the Negev on Tuesday and four more hit the day before, despite Hamas' declaration on Monday that militant factions had agreed to a 24-hour truce.
Hamas: Group ready for truce if Israel sticks to original terms
On Tuesday, senior Hamas official Mahmoud al-Zahar told the Egyptian daily Al-Ahram that "the Palestinians want to give a chance to the Egyptian mediators. Hamas is ready for a truce, if Israel sticks to the terms of the June agreement."
A one-day cease-fire called on Monday "would be extended if positive developments were found," he added.
Officials in the office of Ismail Haniyeh, Hamas' leader in the Gaza Strip, confirmed the remarks.
However, Hamas spokesman Fawzi Barhoum said that while the movement would "study any offer" for a truce, it had not received any so far. And Israeli government and defense establishment sources said that Israel has no intention of conducting new cease-fire negotiations with Hamas at this time.
The Israeli sources confirmed that Egypt is more involved in trying to mediate a truce than it was two days ago. However, they said, it is unclear whether Cairo has enough leverage over Hamas to persuade the organization to reach a deal.
"And before anything else, the [rocket] fire has to stop," added one.
Abbas: Egypt pledges to push for rewnewal of truce
Palestinian Authority Chairman Mahmoud Abbas, who met with Egyptian President Hosni Mubarak in Cairo Tuesday, said afterward that Egypt had pledged to try to convince Hamas and Israel to renew the truce. He also said there has recently been progress in the reconciliation talks between his Fatah movement and Hamas.
Hamas ended its six-month truce with Israel, which began on June 19, last Friday. On Monday, however, it announced it had agreed to an Egyptian request to halt firing for 24 hours to allow the aid convoy to enter the Strip. Virtually all major bakeries in Gaza are currently closed because they lack fuel to run their ovens and flour to bake bread.
However, the Jerusalem Post reported Tuesday that the one-day truce came "after a warning from Egypt that Israel would begin assassinating Hamas leaders if the rockets continued." Quoting an unnamed "senior Hamas official," the daily said Egyptian intelligence chief Omar Suleiman had contacted Hamas leaders in both Gaza and Damascus and urged them to halt the rockets so as not to give Israel an excuse to attack.
IDF troops kill three Gaza militants rigging bomb at border
Meanwhile, the violence continued unabated Tuesday: The Israel Defense Forces killed three armed Palestinians as they were laying bombs along the Israel-Gaza border, while Palestinians fired five Qassam rockets from Gaza into the Negev.
The armed Palestinians threw grenades at the soldiers and set off one bomb before they were killed, but caused no casualties. The rockets also caused no casualties, as all landed in open areas of the Negev. The Democratic Front for the Liberation of Palestine and the Popular Resistance Committees claimed responsibility for the rocket fire.
Also Tuesday, Foreign Minister Tzipi Livni blamed Egypt for Hamas' continuing grip on Gaza. Speaking to the Israel Women's Network in Tel Aviv, she said that "over the last half year, there has not been appropriate monitoring of the Philadelphi Road, which has led to Hamas growing stronger militarily." The Philadelphi Road runs along the Gaza-Egypt border.
Livni plans to raise the issue of arms smuggling from Egypt into Gaza when she meets Thursday with Mubarak in Cairo.