U.S. Secretary of State Condoleezza Rice and Israeli Vice Prime Minister Shimon Peres, meeting in the U.S. capital on Tuesday (August 01) said they believed a ceasefire would shortly be reached in Lebanon. However, despite the shared optimism, the two had a different take on just how soon the campaign against Hizbollah would end. Whereas Rice believed a ceasefire would be reached within days, Peres remained more cynical, saying it was a matter of weeks. Asked by a reporter outside the U.S. State Department when the offensive would end, Peres said: "We don't have an offensive against Hizbollah. We were attacked and we are defending ourselves." "The minute it will stop it will stop. The minute there will be an international force that will control the Southern part of Lebanon, the hostages will be released and the rockets and the missiles will be controlled and Hizbollah will stop being an army within and army. Then we shall have peace. In my judgement it's not far away. You can count it in a matter of weeks, not months," he said. Peres met with U.S. Secretary of State Condoleezza Rice at the State Department ahead of visiting U.S. President George W. Bush at the White House. Peres said he believed a turning point had bee reached in the fighting and that Israel had destroyed a large number of the Hizbollah rockets and missiles. "We feel that there is a turning (point) in the fighting between Hizbollah and ourselves. We feel that our army was able to destroy a great deal of launches and missiles and it's not by accident that the number of the missiles and rockets which are being fired against Israel are going down," Peres said. Israeli airborne commandos battled guerrillas near a Hizbollah-run hospital in eastern Lebanon on Wednesday (August 02), and officials in the Jewish state said the 23-day-old war could run for at least another week. Lebanese security sources said Israeli soldiers had landed by helicopter near the Hizbollah stronghold of Baalbek in the eastern Bekaa valley as aircraft launched dozens of strikes in the region. An Israeli army spokesman declined to comment. Three weeks after the war erupted when Hizbollah seized two Israeli soldiers in a cross-border raid, Israel's security cabinet agreed to step up its offensive, and carry out a ground sweep 6-7 km (4 miles) into Lebanon, a political source said. But U.S. Secretary of State Condoleezza Rice said a ceasefire could be reached within days. "This week is entirely possible. Certainly we are talking about days not weeks," she said on the PBS NewsHour. Despite growing international calls for an end to fighting that has killed at least 624 people in Lebanon and 54 Israelis, Israel was set to resume full air strikes in Lebanon early on Wednesday at the end of a partial, 48-hour suspension. U.N. Secretary-General Kofi Annan urged major powers to patch up differences on the crisis and rescheduled a meeting of potential contributors to an international force for Thursday (August 03). European Union foreign ministers called for an immediate end to hostilities, watering down demands for an immediate ceasefire at the insistence of Britain and other close U.S. allies. British Prime Minister Tony Blair warned Syria and Iran, Hizbollah's main backers, they risked confrontation if they continued to support terrorism and export instability to Iraq and elsewhere. In a speech urging a rethink of the West's strategy to defeat extremism in the Middle East, Blair accused Iran and Syria of helping extreme factions in Iraq and backing militant groups in Lebanon and Palestine. Blair said the international community should tell Syria and Iran that they should either play by the same rules as the rest of the world "or be confronted." "They've done amazing things in that country, that's why it's so tragic what has been brought about - but the only way, whether it's NATO or anybody else, we're going to get an effective multi-national force there is if it has at its heart one principle, which is that our purpose is to make sure that when the Lebanese people vote in their government, in a democracy, they do so without outside interference from Syria or anyone else, and without inside interference by well-armed militia," Blair said in a speech to the World Affairs Council, a nonprofit organisation in Los Angeles. The Prime Minister, who has been heavily criticised at home for siding with the United States over the war between Israel and Hizbollah guerrillas in Lebanon, added that the West must win the battle of democratic values if it is to defeat global extremism. It also needed to work relentlessly "week in, week out" to resolve the conflict between Israel and the Palestinians. Blair was wrapping up a five-day visit to the United States during which he held talks with President George W. Bush in Washington over the Middle East crisis.