Authorities are still searching for Rana, a local politician, who hasn't been seen publicly since the building collapsed. Negligence cases have been filed against him. Police in Bangladesh often detain relatives of missing suspects as a way to pressure them to surrender.
Dhaka police superintendent Habibur Rahman said Rana was a local leader of ruling Awami League's youth front. His arrest, and that of the factory owners, was ordered by Prime Minister Sheikh Hasina, who is also the Awami League leader.
Police said they detained for questioning two engineers working for the Savar municipality, Imtemam Hossain and Alam Ali. They did not say what role they played in approving the design of the building but it was clear that the arrests amounted to a widening crackdown. They spoke on condition of anonymity because they are not authorized to speak to the media.
A garment manufacturers' group said the factories in the building employed 3,122 workers, but it was not clear how many were inside it when it collapsed.
Police say they ordered an evacuation of the building on Tuesday after cracks in Rana Plaza were found, but the factories ignored the order and were operating when it collapsed the next day. Video before the collapse shows cracks in walls, with apparent attempts at repair. It also shows columns missing chunks of concrete and police talking to building operators.
Officials said soon after the collapse that numerous construction regulations had been violated.
The disaster is the worst ever for the country's booming and powerful garment industry, surpassing a fire five months ago that killed 112 people and brought widespread pledges to improve worker-safety standards. Since then, very little has changed in Bangladesh, where low wages have made it a magnet for numerous global brands.
Bangladesh's garment industry was the third largest in the world in 2011, after China and Italy, having grown rapidly in the past decade. The country's minimum wage is the equivalent of about $38 a month.
Among the garment makers in the building were Phantom Apparels, Phantom Tac, Ether Tex, New Wave Style and New Wave Bottoms. Altogether, they produced several million shirts, pants and other garments a year.
The New Wave companies, according to their website, make clothing for several major North American and European retailers.
Britain's Primark acknowledged it was using a factory in Rana Plaza, but many other retailers distanced themselves from the disaster, saying they were not involved with the factories at the time of the collapse or had not recently ordered garments from them.
Wal-Mart said none of its clothing had been authorized to be made in the facility, but it is investigating whether there was any unauthorized production.
AP writers Chris Blake and Gillian Wong in Dhaka, Stephen Wright in Bangkok, Kay Johnson in Mumbai, Matthew Pennington in Washington and AP Retail Writer Anne D'Innocenzio in New York contributed to this report.
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