Possible misconduct by an employee of the administrator assessing compensation under a settlement for the 2010 Deepwater Horizon disaster may have led to BP paying out for “fraudulent, excessive or improper claims”, the company has alleged.

In two letters to Carl Barbier, the judge hearing the civil case over the spill in New Orleans, BP described allegations of “unethical and potentially criminal behaviour” by individuals working for the claims administrator.

Separately, it also highlighted what it called “extremely high costs and low productivity” at the court supervised programme set up to administer the settlement, which was agreed between BP and plaintiffs from the Gulf of Mexico region last year.

In a statement, the company called for an independent investigation into the allegations of misconduct, and for a “comprehensive and public audit of the settlement programme by a reputable national accounting firm”.

It added: “These steps are critical to restoring public confidence in the integrity of the claims process.”

The letters follow a report from the Associated Press that Lionel Sutton, a lawyer who had been working as part of the claims administration programme, had been accused of receiving payments from a law firm representing a claimant.

Following the report, Patrick Juneau, the court-appointed claims administrator, said an internal investigation into the allegations was under way.

Mr Juneau’s office said Mr Sutton had resigned from working for the claims administrator on Friday.

Mr Sutton did not respond to requests for comment.

In one of its letters to Judge Barbier, BP argues that “thus far” Mr Juneau’s investigation of the allegations had been inadequate.

It added that it expected an investigation would “at a minimum” take measures that did not appear to have been taken by the administrator, including collecting and reviewing relevant documents and data, and interviewing individuals that could have knowledge of relevant communications.

In its other letter, discussing what BP sees as wider problems with Mr Juneau’s work, the company said he did not appear to be managing costs effectively.

It added: “The effectiveness, if any, of [the programme’s] procedures to detect and mitigate fraud, waste and abuse is not apparent.”

The new issues raised by BP with Judge Barbier follow rising concern at the company over Mr Juneau’s administration of the settlement, intended to resolve claims for damages from individuals and businesses in five states along the gulf coast who say they were hurt by the spill.

The company argues that Mr Juneau’s interpretation of business losses means it could pay out billions on unexpected and unjustified claims for compensation.

BP originally expected the settlement to cost it $7.8bn; it now expects to have to pay $8.2bn plus the cost of all the business loss claims not yet decided by Mr Juneau.

It has been fighting his interpretation of those claims in the courts, and a hearing is set for the Fifth Circuit appeal court in New Orleans for July 8.

Mr Juneau said in a statement: “We are keenly aware that all parties rightfully expect fairness and objectivity from this claims process.”

He added: “Our goal is to operate in an efficient, transparent and fair manner. All allegations are taken seriously and investigated thoroughly.”

Responding to the concerns raised by BP in its letters, Mr Juneau said: “The proper venue to address these issues is the court. I will continue to do exactly that in this matter.”

He added: “Since June 4, 2012, we have processed claims efficiently and correctly in accordance with the settlement agreement and the orders of the court, as was confirmed in the report by an independent national auditing firm after a thorough and comprehensive audit it recently performed.”

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