BP boss Bob Dudley has told Sky News that he is "willing to settle" the outstanding compensation claims arising from the Gulf of Mexico oil spill in 2010 before they go to court.
A civil compensation trial against BP, involving hundreds of individual lawsuits, will begin in New Orleans on February 27.
In an interview with Jeff Randall, Mr Dudley said: "We continue to meet all our obligations in the US" and added that the company has put aside provisions, some of which had already been paid out in claims.
When asked if the total bill would reach between $20-$25bn, Mr Dudley would not commit to a final figure.
The comments from BP's chief executive came as the firm's profits bounced back following the Gulf of Mexico oil spill, recording total profits of £15.1bn ($23.9bn) for 2011.
The London-based company suffered a loss of £3.1bn ($4.9bn) in 2010 when an explosion on the BP-leased Deepwater Horizon rig killed 11 workers, caused millions of barrels of oil to leak into the sea and left the company with huge compensation costs.
BP's profits for the fourth quarter of last year rose to £4.9bn, helped by higher oil prices. It was more than forecasted and a 38% increase on a year earlier.
Replacement cost profit, a closely watched industry measure, was £3.1bn ($5bn).
The profits for the final three months of 2011 exceeded those of rival oil giant Shell (LSE: RDSB.L - news) , which made £4.1bn over the same period. But Shell's full year profits were up to £18.1bn.
The turnaround in profits comes as BP prepares for a civil compensation trial in New Orleans in the US over the beginning on February 27.
But two years on from the Gulf of Mexico oil spill disaster, it is facing hundreds of lawsuits.
If the company is found guilty of gross negligence it could be liable for tens of billions of dollars in fines and other payouts. They could face a fine of £2,720 ($4,300) per barrel spilled under the Clean Water Act.
Mr Dudley said BP was preparing "vigorously" for the lawsuits.
The firm was ready to settle on "fair and reasonable terms" but was also ready to fight, he said.
BP said that it had committed £632m ($1bn) "for the early restoration of natural resources following the Deepwater Horizon accident in 2010."
The company added that by the end of 2011 it had paid more than £4.9bn ($7.8bn) to meet claims and government payments, while £9.5bn ($15.1bn) had been paid into the trust fund used to compensate victims of the oil spill disaster.
Mr Dudley said: "BP is on the right path.
"2012 will be a year of increasing investment and milestones as we build on the foundations laid last year."
BP shares are down by a quarter since the oil spill.
It resumed deep water drilling in the Gulf of Mexico last year, a welcome move for the oil firm after a deal with Russia's Rosneft to drill in the Arctic fell apart.
In his interview with Jeff Randall, the BP boss also defended the City's bonus culture, saying London needed to remain competitive globally.
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