The Australian government said on Tuesday that PTTEP was "under a lot of pressure" to control the blaze and stop the flow of oil.
"It's clearly had an impact on the standing of the oil and gas industry in Australia," Martin Ferguson, Australia's minister for resources and energy told ABC Radio.
Ferguson said that once the spill was contained, he would launch an inquiry and, if the rig operator was "found to have been at fault with respect to any of their responsibilities, then any potential action will be appropriately considered at the time".
According to PTTEP, the blaze on the West Atlas rig broke out as a mixture of dense mud was being pumped from another nearby rig via a separate shaft in an effort to plug the leaking well.
"What we're trying to do is to stop it by injecting heavy mud into the relief well," Jose Martins, the company's chief financial officer told ABC Radio.
He said that engineers had prepared about 4,000 barrels of the mixture, adding that it should be possible to extinguish the fire soon after the mud goes in.
Martins said the engineers working on tackling the leak were "the world's best".
"One we get rid of the source, the fuel for the fire, then obviously we can bring in the fire-fighting equipment and hopefully control the fire that way."
Amir Murad, general manager of the Petroleum Industry of Malaysia Mutual Aid Group, an organisation that responds to oil spills in Malaysian waters, told Al Jazeera the top priority was putting out the fire.
"If the rig collapses it will turn into a situation where sea water will enter the area where the blaze started, hence putting out the fire," he said.
"But there still remains a risk of more oil going into the sea."
The rig began leaking oil on August 21 spewing between 400 and 2,000 barrels of crude into the Timor Sea each day.
According to the World Wildlife Fund (WWF), hundreds of seabirds have died after coming into contact with the toxic slick, while dolphins, whales and other marine life are also being exposed to the spill.
Paul Gamblin, a WWF policy advisor based in Australia, said the spill had produced a "chemical cocktail" that could have a long-term impact on the region's wildlife.
Speaking to ABC radio he said the area around the rig was a "very near pristine environment" which had now been contaminated with upwards of five million litres of toxic substances.
On Tuesday, Senator Bob Brown, the head of Australia's Green party's, repeated calls for the government to take tougher action and demanded Martin Ferguson's resignation over his handling of the incident.
"He has completely bungled one of the biggest environmental catastrophes the Commonwealth government has had to deal with," Brown told local media.
"He is an oil industry parrot and he should resign."
Ferguson said previously that the oil would "evaporate naturally" and that he was proud of the oil industry's environmental record.