Israel began its first shipment into Gaza on Tuesday since it imposed a blockade on the impoverished territory last week in response to a sharp increase in rocket attacks by Palestinian militants. Israel pumped cooking oil and fuel for Gaza's power plant through the Nahal Oz crossing. Later in the day it is expected to allow a single shipment of fuel, food and medicine into Gaza through the Kerem Shalom crossing. With the rate of Kassams striking the western Negev down from 50 a day at the end of last week to just a few on Monday, and facing immense international pressure, Israel will begin easing its siege on Gaza Tuesday morning and allow shipments of fuel and humanitarian supplies. The decision follows a day of outcry from the Arab world, threats by the Palestinian Authority to end diplomatic negotiations, warnings by UN organizations that food aid would have to be suspended, and criticism from friends, such as visiting Dutch Foreign Minister Maxime Verhagen. Defense Minister Ehud Barak decided Monday night to let in a shipment of 2.2 million liters of diesel fuel for Gaza's power plant, giving it the capacity to generate 60 megawatts for a week. Israeli and Egyptian power grids supply Gaza with an additional 140 megawatts of power. In addition, some 500,000 liters of diesel for hospital generators will be brought into the Gaza Strip, and 50 trucks full of humanitarian aid, from medical supplies to vital food items, will be allowed in, 13 of those trucks from Jordan. Despite the decision to ease the siege, Barak, speaking Monday night at the Herzliya Conference, said Israel needed to intensify its activity against Gaza until the peace and security of Sderot and the Negev areas around the border were guaranteed. "We have to put pressure and more pressure on Gaza," Barak said. "Our concern has to be quiet for the residents of the western Negev and Sderot. If this silence requires a large noise on the other side, there will be noise." Barak said that while he knew this was difficult, "I am more concerned about our [well-being] than theirs." He pledged that the IDF would find a technological and military solution to the Kassam rockets. Earlier in the day, Barak spoke to Egyptian President Hosni Mubarak and assured him that Israel had no interest in creating a humanitarian crisis in Gaza. At the same time, he said that Israel would not allow the Palestinians to fire rockets into the western Negev. Mubarak also spoke to Prime Minister Ehud Olmert, and warned him about a dire humanitarian crisis in the making. Defense officials warned that if Hamas renewed its bombardment of the Negev - last week over 160 Kassam rockets were fired at Sderot - Barak would immediately reimpose the tight closure and cut off all supply lines to Gaza. "It is up to Hamas," an official said. "If they want supplies they need to stop the rockets." While the Palestinians warned Monday of an imminent humanitarian crisis, senior defense officials said that Israel was carefully watching the developments in Gaza and that the situation was far from dire. "They have enough food for several more days and the new fuel supply will allow them to activate the power plant," said a senior defense official. "Even without the new fuel supply they have enough electricity for more than half of Gaza since Israel regularly supplies Gaza with 70 percent of its needed electricity." Foreign Ministry spokesman Aryeh Mekel said that the decision to ease the restrictions came about because of the drastic decrease in Kassam fire. Mekel said the decline in rocket fire showed that Hamas could, when it wanted, control the rocket fire. He said that the rate of Kassam fire in the last few days showed that Hamas "got the message." Olmert, in a speech to the Kadima faction, said that Israel would not allow a humanitarian crisis to break out in Gaza. At the same time, he said that Israel would not tolerate a situation where Sderot residents were gripped by fear day and night, while life in Gaza proceeded normally. "We will not allow a humanitarian catastrophe, but we have no intention of making their lives easier," Olmert said. "As far as I'm concerned, the residents of Gaza can walk, and they will not get gasoline because they have a murderous, terrorist regime that does not allow the residents of southern Israel to live in peace." Olmert, in his phone conversation with Mubarak and during his meeting with Verhagen, said that Hamas was exaggerating the level of the crisis in order to apply international pressure on Israel. Foreign Ministry officials said that Hamas orchestrated Sunday night's blackout in Gaza, and suspected that this was done in cahoots with the Arab media outlets, which devoted a great deal of time to the issue and had commentators already on the scene to provide analysis. Officials said that Verhagen, in meetings with Olmert and Foreign Minister Tzipi Livni, spoke out against the siege, and said that Israel's reactions to the rocket attacks needed to be proportional. The officials said that Verhagen was more understanding of Israel's targeted attacks on terrorists inside Gaza than of the closure and its effects. Verhagen visited Sderot with Livni, and saw and heard first hand the anxiety of the residents there. "I was able to witness myself the terrible result of continuing mortar and rocket attacks, and the fear of innocent civilians living there with their children trying to have just a normal life," he said. "It is absolutely clear there is no excuse for these despicable acts of terrorism." At the same time, the Dutch foreign minister said that the people of Gaza should not be punished and that plunging them into "darkness, poverty and suffering" will only breed more violence. Meanwhile, Israeli diplomatic officials said they were not certain whether Livni would continue negotiations with Palestinian negotiator Ahmed Qurei this week. Palestinian officials said they were considering a suspension of the talks because of the situation in Gaza. Livni, however, said it was clear from the outset that the ongoing negotiations would "take place in the shadow of the war on terrorism." She said that "activity vis-Ã -vis the moderates will take place while responding to the ongoing daily threat coming from the Gaza Strip." Livni said that Israel was committed to maintaining the humanitarian situation in the Gaza Strip, and that the Jewish State "is the only place in the world that supplies electricity to terrorist organizations that launch rockets at it in return. Life for the Palestinians in the Gaza Strip is not easy because there is terrorism there, and this should be crystal clear: Hamas can change the lives of the people in Gaza in an instant, if it ceases terrorism. It knows that, and the Palestinian civilians must understand it as well." Before the decision to ease the siege, international aid organizations warned that they would be forced to suspend food distribution by the end of the week because of a shortage of fuel and plastic bags used to pack food. "We are going to have to suspend operations on Thursday or Friday," said Chris Gunness, spokesman for the United Nations Relief and Works Agency, which distributes food aid to 860,000 Palestinian refugees in Gaza. The World Food Program, which gives food to another 270,000 Gaza residents, said it would also have to suspend distribution by Thursday, because they expected their fuel used to power distribution trucks to run out. Tovah Lazaroff and AP contributed to this report.