MADRID, Dec 28 (Reuters) - Demand for free COVID-19 testing kits provided by Madrid"s regional government far outstripped supply on Tuesday, with long queues forming outside pharmacies as nationwide infections continued to climb amid the Omicron variant"s rapid expansion. Spain"s coronavirus infection rate hit a new record, rising to 1,360 cases per 100,000 people, measured over the preceding 14 days, from 1,206 cases reported on Monday, a five-fold rise since the beginning of December, according to health ministry data. read more Around 250 new deaths in the past seven days were reported on Tuesday, bringing the total to 89,253. But hospitals remained under much less strain than in previous waves of the pandemic as the government reported that 80% of the population older than 60 had received a booster vaccine dose. Madrid-based pharmacist Cristina Sanchez said she had only received 20 test kits to distribute on Tuesday as part of a plan to reinforce supply after pharmacies started running out of paid tests, but there were already more than 30 people waiting outside when she opened. As the first few people in line tend to take several tests each, most have to return home empty handed or buy kits for 9 euros, which were also selling out fast. "The people who are waiting outside, who are cold, who have been waiting for a long time, we can"t give them to them anymore," she told Reuters at her pharmacy on the outskirts of Madrid. Taxi driver Miguel Jesus Arroyo was one of the lucky few to secure a test. "You"ve got to get up early, because if you don"t come soon, it"s all over in a flash," he said. Italy, one of the countries worst hit by the pandemic, has also reported rising infections and long lines have developed at some drive-in testing centres while many chemists have reported being deluged with requests for tests. read more Luca Zaia, the head of the north-eastern Veneto region which has been badly hit by the surging case load, said he was worried test kits could soon run out and asked the government to drop testing requirements in certain situations. "We cannot let the testing system collapse," he said.