Woolworths is again under pressure to sign a voluntary safety accord following another fatal fire at a Bangladesh clothing factory this week.
Target and Big W have confirmed they have sold goods linked to the factory in which at least nine people died, and Woolworths is currently investigating whether it has done the same.
Target has already designed to prevent such incidents and Woolworths is promising to sign it.
But Woolworths is being less clear about whether it actually buys garments from Bangladesh, despite telling consumers that it does not.
Seven weeks ago Woolworths told a customer on Facebook it did not buy clothes made in Bangladesh, but when questioned by The World Today the company was less certain.
A Woolworths spokeswoman said the statement was true at the time.
She said it would take some time to determine if the company does buy clothing from Bangladesh or not.
Oxfam spokeswoman Daisy Gardener says this week's fire is more reason for Woolworths to sign up to the accord as soon as possible.
"Woolworths, who own Big W, they said that they were going to sign the accord but they haven't yet so we're really hoping that this latest fire is a big wake-up call for Woolworths," she said.
"We think they need to sign on as soon as possible so that they are added into the list of factories that will be inspected. There's absolutely no point in waiting around."
Oxfam also want Pacific Brands, who owns Bonds Underwear and Rivers, Best and Less and Just Jeans, to sign the Bangladesh accord.
Low wages make Bangladesh one of the cheapest places in the world to make clothes, but critics say safety shortcuts are also part of the deal.
The new safety standards drafted by unions, companies and the Bangladesh government include mandatory safety inspections, and allow people to turn down work in unsafe buildings.
A report can result in an immediate safety inspection and evacuation.
About 1,600 factories have signed up so far but the crucial independent inspectors have not yet been hired.
The huge fire at the Bangladeshi factory, whose workers were making clothes and fabrics for top Western labels, killed seven people and injured dozens more.
Firefighters battled through the night on Tuesday (local time) to douse the flames at the Aswad Knit Composite factory at Sripur, on the outskirts of the capital Dhaka.
Parts of the two-storey building were still smouldering early on Wednesday.
Police said the fire, which broke out when most of the 3,000 workers had left, was so intense that most of the bodies were too badly burned to be identified.
Both Gap and H&M denied that they had placed orders for clothes at the factory, but said they had a supplier relationship with its owner Palmal Industries, one of the country's largest garment groups.
The collapse of the infamous in April killed 1,129 people.