The Deepwater Horizon oil rig burns in the Gulf of Mexico more than 50 miles southeast of Venice, La. in 2010. (AP Photo/Gerald Herbert, File)

Halliburton has agreed to pay as much as $1.1 billion to settle most plaintiffs’ claims for damages stemming from its role in the Gulf of Mexico oil spill, its lawyers said in court papers Tuesday.

The Houston-based oil services company was BP’s cement contractor on the Deepwater Horizon drilling rig, which caught fire and exploded on April 20, 2010. The accident killed 11 men and caused the worst environmental disaster in U.S. history.

If approved by a federal judge in New Orleans, the new settlement — which was agreed to by attorneys for Halliburton and the plaintiffs in a class-action suit — would mean that some claimants who have already won money from BP could be in line for extra compensation.

It also would limit the potential hit for Halliburton, which is awaiting a ruling from U.S. District Judge Carl Barbier on the extent of its liability in the case, a decision with big implications for how much the company owes claimants.

BP is bracing for that ruling as well, but it has not worked out any kind of cap on how much it may ultimately have to pay out to individual landowners, businesses and local governments that suffered losses when oil washed up on their property.

Claimants could still choose to opt out of Halliburton’s settlement plan and litigate on their own. But legal experts say that would be a costly and time-consuming strategy.

And those who agree to the settlement would get some money in damages even if Barbier eventually rules that Halliburton’s actions were not a major factor leading to the disaster.

Joe Rice, a negotiator on the settlement for the plaintiffs, called the deal “a reasonable compromise of a highly contested issue,” adding, “We are pleased to have finally come to terms which both parties are able to accept.”

Stephen Herman and James Roy, lawyers for the plaintiffs’ committee that brokered the agreement, said in a statement Tuesday that Halliburton “stepped up to the plate and agreed to provide a fair measure of compensation to people and businesses harmed in the wake of the Deepwater Horizon tragedy.”

Assuming Barbier approves the deal, a court-appointed administrator would carry it out, according to the 51-page settlement filed with the court Tuesday.

A special master also would be appointed to determine how much of the $1.1 billion will be used to pay claims that have already received or will receive compensation in BP’s settlement, and how much will be used to pay claims for punitive damages.

Since it opened in June 2012, the claims facility handling BP’s settlement program has processed almost 295,300 claim forms, federal court documents show. As of Aug. 1, the program had issued eligibility notices affirming the validity of more than 69,300 claims, with payment offers totaling more than $5 billion.

But BP has since challenged the validity of that agreement. It has asked the U.S. Supreme Court to rule that businesses must prove that the spill caused them financial losses before they can collect money from the multibillion-dollar settlement. That argument has been rejected by the district and appellate courts.

Meanwhile, Halliburton has already pleaded guilty to a misdemeanor charge of destroying evidence in connection with the spill. As a result, it agreed to pay a maximum $200,000 fine, serve five years of probation and donate $55 million to the National Fish and Wildlife Foundation.

Transocean, another company involved in the spill, has agreed to pay $1.4 billion in civil and criminal fines and penalties, mostly to resolve federal Clean Water Act civil penalty claims.

In November 2012, BP itself agreed to plead guilty to 11 counts of felony manslaughter, obstruction of Congress and a series of environmental crimes, and to pay a $4 billion fine.

Follow Richard Thompson on Twitter, @rthompsonMSY.