The last Israeli troops left the Gaza Strip before dawn Wednesday, the military said, as Israel dispatched its foreign minister to Europe in a bid to rally international support to end arms smuggling into the Hamas-ruled territory. The timing of the pullout reflected Israeli hopes to defuse the crisis in Gaza before President Barack Obama entered the White House. The military said troops remain massed on the Israeli side of the border and are poised to take action if militants violate a fragile three-day cease-fire. The troops' exit marked the end of an Israeli offensive that ravaged Gaza and left a total of 1,284 Palestinians dead and 4,336 wounded, according to the Palestinian Center for Human Rights. The rights group, which has dispatched researchers to collect the names of the dead, said 894 of those killed were civilians. The Israeli military says 500 Palestinian militants were killed in the fighting. Gaza's militant groups claim only some 150 of the dead were armed fighters. Israel launched the offensive to permanently halt years of militant rocket fire on growing numbers of Israelis and to halt the smuggling of arms that turned Hamas into a potent threat to much of southern Israel. But by Wednesday, some of the tunnels on the Egyptian border appeared to be back in business, with workers clearing blocked passageways, bulldozers carrying out other repairs, and fuel already being brought from Egypt into Gaza, according to AP Television News footage. Israeli Foreign Minister Tzipi Livni was heading to Brussels on Wednesday, hoping to clinch a deal committing the European Union to contribute forces, ships and technology to anti-smuggling operations, Israeli officials said. Last week, the U.S. signed an anti-smuggling deal with Israel calling for expanded intelligence cooperation between the two countries and other U.S. allies in the Middle East and Europe. Gaza remained tense Wednesday. Israeli navy ships fired rounds of machine-gun fire at the beaches of northern Gaza, and the military said a Gazan fishing vessel had strayed into an area declared off-limits by the Israeli navy. The death toll in Gaza has provoked international outrage. In Israel, however, the war has strong backing, because it is seen as a legitimate response to militants who now have one-eighth of the population within rocket range. U.N. Secretary-General Ban Ki-moon left the region early Wednesday after touring Gaza and southern Israel. Ban called for an investigation into the Israeli shelling of U.N. compounds in Gaza during the fighting, which he termed "outrageous." He also called militant rocket attacks against Israel "appalling and unacceptable." The Israeli military said it has launched an internal investigation into allegations about its use of white phosphorus munitions. U.N. officials and human rights groups have alleged Israel used such weapons, typically employed to illuminate targets or create smoke screens. Amnesty International has said Israel's firing of white phosphorus shells in densely populated residential areas of Gaza is a war crime. Both sides declared cease-fires that went into effect Sunday, but the arrangements remain shaky. Israel reported mortar shelling from Gaza on Tuesday, and the Palestinians say Israeli troops shot and killed two Gaza farmers along the border after the truce took hold. The fighting ended before Israel achieved its aims, though world leaders have pledged to assist in efforts to keep militants from restocking war-depleted arsenals. The U.S. has promised to supply detection and surveillance equipment, as well as logistical help and training to Israel, Egypt and other nations in the region. The equipment and training would be used to monitor Gaza's land and sea borders. The Israeli-American agreement also calls for the U.S. to expand work with its NATO partners, particularly in the Red Sea, Mediterranean Sea, Gulf of Aden, Indian Ocean and eastern Africa. At the signing ceremony in Washington, Livni described the deal as "a vital complement for a cessation of hostility" in the troubled region. Shortly after, she said she hoped European countries, notably Britain, France and Germany, would work out similar agreements with the Israelis. Although signed by the Bush administration on its last working day, the agreement is binding on the Obama administration. Most of the smuggling was carried out through tunnels underneath the eight-mile (15-kilometer) border between Egypt and Gaza border. Egypt has proved unable or unwilling to halt the flow of weapons and medium-range rockets coming through the tunnels, alongside fuel and consumer goods. Israel bombed most of the tunnels during the offensive. Iran, one of Hamas' main backers, rejected the international attempt to deny the militant group weapons. In statements reported Wednesday on the Web site of Iranian state TV, Foreign Minister Manouchehr Mottaki said that as Israel is well-armed, it would be wrong to question the Palestinians about obtaining weapons. Israel says Iran provides the group with cash, weapons and training. Tehran denies giving any weapons to Hamas.