* Official says 41 people found alive late on Thursday
* Around 1,000 people still unaccounted for; death toll hits 273
* Police say building owner on the run
* Factories made garments for brands in Europe, North America
By Serajul Quadir and Ruma Paul
DHAKA, April 26 (Reuters) - The search for survivors from Bangladesh's worst industrial accident stretched into a third day on Friday, with the death toll rising to 273 after the collapse of a building housing factories that made low-cost garments for Western brands.
Almost miraculously, 41 people trapped inside the rubble of the eight-storey building were rescued alive late on Thursday, government minister Jahangir Kabir Nanak said, about 40 hours after the disaster on the outskirts of Dhaka.
Nanak said they had been working on the fourth floor of the Rana Plaza building and had all been found trapped in one room. Few other details were available.
Around 2,000 people have been rescued over the past two days, at least half of them injured, but as many as 1,000 people remain unaccounted for.
An industry official has said 3,122 people, mainly female garment workers, were inside the building despite warnings that it was structurally unsafe.
Rescuers from Bangladesh's army, navy and air force, as well as police and fire services, pored over huge piles of rubble and twisted metal in the search for survivors, using their bare hands as well as mechanical equipment.
"We are not sure how many people are still trapped under the rubble," said Dhaka District police chief Habibur Rahman, who updated the death toll early on Friday to 273. "Priority has been given to save people who are still alive," he said.
Wednesday's disaster refocused attention on Western high-street brands that use Bangladesh as a source of low-cost goods.
North American and European chains, including British retailer Primark and Canada's Loblaw, said they were supplied by factories in the Rana Plaza building, which is in the commercial suburb of Savar, about 30 km (20 miles) from the capital.
Savar residents and rescuers dropped bottled water and food on Thursday night to people who called out from between floors.
Relatives identified their dead among dozens of corpses wrapped in cloth on the veranda of a nearby school.
Police said the owner of the building, Mohammed Sohel Rana, a local politician from the ruling Awami League, was told of dangerous cracks on Tuesday.
While a bank in the building closed on Wednesday because of the warnings, the five clothing companies told their workers there was no danger, industry officials said. Rana is now on the run, according to police.
"We asked the garment owners to keep it closed," said Bangladesh Garment Manufacturers and Exporters Association (BGMEA) President Mohammad Atiqul Islam.
Despite the overnight rescue of 41 people, officials conceded the chances of finding more alive were growing slimmer.
"We can't be certain of getting them all out alive. We are losing a bit of hope," fire brigade rescue worker Mizanur Rahman said earlier on Thursday.
Special prayers will be offered at mosques, temples and pagodas across Bangladesh on Friday for the dead, injured and missing. The government declared a national day of mourning and flags were flown at half mast at all official buildings.
Anger over the working conditions of Bangladesh's 3.6 million garment workers, the overwhelming majority of them women, has grown steadily since the building collapse.
More than 1,000 textile workers besieged the BGMEA on Thursday, pelting it with stones and clashing with riot police. The workers demanded all garment factories be shut and the owners harshly punished for accidents.
Bangladesh is the world's second-largest apparel exporter, with the bulk of exports - 60 percent - going to Europe. The United States takes 23 percent and Canada takes 5 percent.
Primark, a unit of Associated British Foods, has confirmed one of its suppliers occupied the second floor of the building. Danish retailer PWT Group, which owns the Texman brand, said it had been using a factory in the building for seven years.
Canada's Loblaw, a unit of food processing and distribution firm George Weston Ltd, said one factory made a small number items for its "Joe Fresh" label.
Primark, Loblaw and PWT operate under codes of conduct aimed at ensuring products are made in good working conditions.
Documents including order sheets and cutting plans obtained by Reuters appeared to show that other major brands such as Benetton had used suppliers in the building in the past year.
A Benetton spokesman said none of the factories were suppliers to the company. Spain's Mango said it had an unfulfilled sample order at the plaza with Phantom Apparel.