British Prime Minister Tony Blair welcomed a draft United Nations resolution Saturday as likely to inspire a cease-fire between Israel and Hizbullah within the next few days. "It is an important breakthrough," Blair said of draft resolution agreed by the United States and France and presented to other UN Security Council members. "And it should mean that, on the adoption of the resolution by the full Security Council, there is then a full cessation of hostilities at that point by both sides," said Blair, who has spent the past few days talking with international leaders about reaching such an agreement. Blair, delivering a prepared statement in his 10 Downing St. office, said passage of the resolution should permit "the cessation of hostilities literally within the next couple of days." He said installing an international peacekeeping force in southern Lebanon would "allow us to deal with the underlying issue, and put the government of Lebanon fully and properly in control of the whole of the Lebanon." Blair declined to answer questions. Earlier, in a written statement, Blair cautioned that world leaders "cannot and must not lose sight of the Palestinian dimension, which is the root cause of this conflict. I will work tirelessly to re-energise the Middle East peace process, which is the only way to provide a viable, long-term solution to this situation, with a Palestinian state alongside a secure Israel." As he spoke, tens of thousands of people, chanting and waving Lebanese flags, marched through London to demand an immediate cease-fire. Police said 15,000 people joined the march from HydePark past the US Embassy and on to Parliament. Organizers - a coalition of peace, Muslim, Palestinian and Lebanese groups - put the turnout at more than 100,000. "The demonstration shows the unity of any normal thinking person in this country that there should be an immediate cease-fire and that the government's line is incomprehensibly wrong," said Jeremy Corbyn, a lawmaker from Blair's Labor Party. Many protesters carried Lebanese flags or placards, some critical of Israel and demanding an end to occupation of the West Bank. Veteran peace campaigner Bianca Jagger, walking at the head of the march, said the protest was not anti-Israel. "I support the existence of Israel, and I think we are wrong to say otherwise," she said. "But watching the images of innocent children dying as we have been for the last 24 days does not promote a peaceful solution in the region." Blair postponed his summer vacation Friday so he could stay in London and work toward an end to fighting. Aides said he discussed the wording of proposed UN resolution to stop the fighting on Friday with Prime Minister Ehud Olmert, French President Jacques Chirac, UN Secretary-General Kofi Annan and other leaders, and met with a delegation of Lebanese officials. A spokesman said Blair was spending Saturday on the telephone and in briefings on the diplomatic and humanitarian situation in the Middle East. He said Blair had spoken to Lebanese Prime Minister Fuad Saniora and restated his support for the seven-point cease-fire plan put forward by Saniora at last week's crisis summit in Rome. The plan calls for a mutual release of prisoners by Israel and Hizbullah and the withdrawal of IDF troops from southern Lebanon. It foresees the Lebanese government taking control of southern Lebanon with the help of an international force. Work and Pensions Secretary John Hutton on Saturday denied reports of a rift within Blair's cabinet over the prime minister's refusal to call for Israel to halt its offensive in Lebanon. "I think the government is very strongly behind what the prime minister is trying to do here, which is to find a way to build, yes, an immediate cease-fire that ends the death and destruction... but then puts in place a process where we can allow the peace and security in the region to begin again," Hutton told BBC radio.