NEW ORLEANS (AP) -- BP's (NYSE:BP) cement contractor on the drilling rig that exploded in the Gulf of Mexico in 2010 says it is trying to negotiate a settlement over its role in the disaster.

Halliburton (NYSE:HAL) Chief Financial Officer Mark McCollum said during a conference call Monday that talks are at an "advanced stage." The Houston-based company says it hopes to resolve a substantial portion of private claims spawned after the explosion of the rig Deepwater Horizon.

Testimony ended last Wednesday in the first phase of a trial over the blast, which killed 11 workers and triggered the nation's worst offshore oil spill.

A federal judge in New Orleans ultimately could decide how much more money BP, Halliburton, and rig owner Transocean (NYSE:RIG) owe for their roles in the catastrophe.

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