BP begins a year-long trial in the US on Monday over the 2010 Deepwater Horizon explosion and oil spill in the Gulf of Mexico.
The oil giant will defend itself against charges of gross negligence in America's worst environmental disaster that killed 11 men.
BP faces a fine of up to $17.6bn, the biggest in history, as it goes against the US and Gulf states that were affected by the spill and the Department of Justice.
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The US and Gulf states were said to be considering a $16bn out of court settlement with BP over pollution fines and natural resource damages claims, according to The Wall Street Journal.
Investors reacted positively to the possibility of a settlement, as shares climbed 2.08% to 453.30p in afternoon trading, following three weeks of decline.
The trial, held in New Orleans, is divided into two parts. The first phase will focus on the causes of the accident, who should be held responsible, and to what degree. The second will deal with penalties in relation to the amount of oil spilled.
Other parties included in the trial for their role in the tragedy are contractor Halliburton, rig operator Transocean, and Cameron, which manufactured the blowout preventer meant to stop oil leaks.
BP has said it was willing to settle on "reasonable terms" but would fiercely refute claims of gross negligence.
"This was a tragic accident, resulting from multiple causes and involving multiple parties. We firmly believe we were not grossly negligent," Rupert Bondy, Group General Counsel of BP, said in a statement last week.
Bondy highlighted the group's efforts in paying settlements to partners, contractors, the Public Service Commission and the US federal government.
In November BP agreed to pay $4.5bn to settle criminal charges relating to the spill.
Bondy also suggested the government's public estimate of 4.9m barrels of oil released was at least 20% overstated.
He said BP should be excluded from 810,000 barrels of oil that was captured from the Macondo reservoir, which could potentially reduce its final fine by as much as $3.5bn.
"BP believes that a figure of 3.1m barrels should be the uppermost limit of the number of barrels spilled that should be used in calculating a Clean Water Act penalty."
A day ahead of the trial, the company was bumped up on this year's list of top UK 'Consumer Superbrands'. It gained the 18th position, up from last year's 35th spot, according to the annual Superbrands UK survey which named Rolex the winner.
BP also joined the survey's 'Business Superbrands' list this year in 11th place. Apple received topped the list while receiving second place on the 'Consumer Superbrands' list.
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