NEW ORLEANS (AP) — BP's cement contractor on the drilling rig that exploded in the Gulf of Mexico in 2010 announced Monday that it is trying to negotiate a settlement over its role in the disaster, a focus of trial testimony that ended last week.

Halliburton Chief Financial Officer Mark McCollum said during a conference call to discuss first-quarter earnings that talks were at an "advanced stage." The Houston-based company says it hopes court-facilitated negotiations will resolve a substantial portion of private claims it has faced since the Deepwater Horizon rig blast spawned the nation's worst offshore oil spill.

"We are working hard to come to a reasonable settlement that would be in the best interest of our shareholders," Halliburton president and CEO Dave Lesar said on the same call.

Testimony ended last Wednesday for the first phase of a trial over London-based BP PLC's Macondo well blowout. The April 20, 2010, blowout triggered an explosion that killed 11 workers and spilled millions of gallons of oil into the Gulf.

U.S. District Judge Carl Barbier in New Orleans presided over the trial without a jury and heard eight weeks of testimony. Barbier, who isn't expected to rule for several months, ultimately could decide how much more money BP, Halliburton and rig owner Transocean Ltd. owe for their roles in the catastrophe.

Halliburton and BP have blamed each other for the failure of the cement job to seal the Macondo well. During the trial, BP asked Barbier to sanction Halliburton for allegedly destroying evidence about the role that its cement slurry design could have played in the blowout.

After the trial started on Feb. 25, Halliburton discovered cement samples at a Lafayette laboratory that weren't turned over to the Justice Department for testing after the spill. Halliburton lawyers called it a "simple misunderstanding" and accused BP of trying to create a "sideshow."

Plaintiffs' attorneys accused Halliburton of using leftover cement that contained a destabilizing additive in an effort to save time and money. They also claimed Halliburton employees conducted "off-the-record" cement tests and didn't write down some test results because they feared how they could affect spill-related litigation.

David Uhlmann, a University of Michigan law professor and former chief of the Justice Department's environmental crimes section, said the damaging testimony gave Halliburton added incentive to settle.

"Halliburton is certainly worse off as a result of the trial because the trial highlighted the degree to which their conduct during the spill and during the litigation has been problematic," he said. "They looked terrible."

Uhlmann said a settlement may not preclude Barbier from imposing the sanctions BP is seeking for Halliburton's handling of evidence.

Halliburton said its most recent settlement offer included an unspecified amount of both stock and cash. McCollum said the company believes it has "substantial legal arguments and defenses against any liability" and is "fully prepared to see this matter to conclusion in the courts" if the talks don't produce an agreement.

Halliburton wouldn't identify the party or parties with which it is trying to reach a settlement, but the Plaintiffs' Steering Committee is the team of private lawyers for Gulf Coast businesses and residents who claim the spill cost them money. The committee's members negotiated a multibillion-dollar settlement with BP more than a year ago.

Committee spokesman David Falkenstein said in a statement that it doesn't comment on the "existence or non-existence of settlement discussions."

The Justice Department didn't sue Halliburton but has reached separate settlements with BP and Switzerland-based Transocean. The states of Alabama, Florida, Louisiana, and Mississippi also have filed spill-related lawsuits.

Meanwhile, a court-appointed claims administrator can continue making payments to businesses affected by the 2010 oil spill while BP appeals a judge's decision in a dispute over the payouts.

A three-judge panel from the 5th U.S. Circuit Court of Appeals on Monday rejected BP's request for a stay of an April 5 order by Barbier.

Barbier refused to block what could be billions of dollars in settlement payouts to businesses that claim the spill cost them money.

The judge already had upheld claims administrator Patrick Juneau's interpretation of settlement terms governing payments to businesses. BP argued that Juneau has exposed the company to paying for fictitious losses.

The 5th Circuit agreed Monday to expedite BP's appeal of Barbier's ruling.