GAZA, Sept 26 (Reuters) - The reconstruction of homes in Gaza that were destroyed or damaged in the May conflict between Israel and Hamas will begin in the first week of October using aid from Qatar, a senior Palestinian housing official said on Sunday. Gaza"s Hamas-run government says Israeli air strikes destroyed about 2,200 homes in the enclave during the 11-day conflict and damaged 37,000 others. Some homes in Israel were damaged by rockets launched by Islamist organisation Hamas and other Gaza militant groups. About 1,800 destroyed or damaged homes will be rebuilt in the first phase of work, according to Naji Sarhan, Gaza"s deputy minister for housing and public works. He said that Israel had lifted some restrictions on steel and cement entering the territory in recent days. Last week, Egypt began repairing Gaza"s main coastal road, part of a broader plan to revamp Gaza infrastructure. Palestinian officials say 250 people, including 66 children, were killed by Israeli air strikes on Gaza. Israeli officials says 13 people, including two children, were killed in Israel by militant rockets. Following a May 21 ceasefire, mediated by Egypt, access to reconstruction funds and materials has been a key Hamas demand . Israel limits construction materials entering the territory, saying Hamas uses them to build weapons to wage attacks. But following an agreement with the United Nations and Qatar, Israel allowed about $20 million in aid from the Gulf state to enter Gaza this month. That disbursement will be followed by $50 million of Qatari funds earmarked for rebuilding homes, Sarhan said. Gaza officials estimate it will take $479 million to rebuild homes and infrastructure damaged in the May fighting. Qatar and Egypt have each pledged $500 million for Gaza reconstruction.