The trial had been scheduled to begin Monday morning in a New Orleans federal court.
Those suing are seeking to determine the culpability of BP and other companies for the explosion that killed 11 and unleashed an 87-day oil spill, the largest offshore spill in U.S. history.
Later phases are supposed to determine how much oil escaped from the well in the Gulf of Mexico and how successful the companies involved were at containing and cleaning it up.
BP and lawyers representing about 120,000 individuals and businesses who say the spill harmed their livelihoods announced Sunday afternoon that
U.S. District Judge Carl Barbier had adjourned the trial for a week to give them more time to work toward an out-of-court agreement. "There can be no assurance that these discussions will lead to a settlement agreement," the parties said in a statement.
The settlement talks don't appear to include the other parties in the complex case, such as the U.S. government, which plans to argue that BP was "grossly negligent" in the disaster and should be subject to stiff civil penalties. The Department of Justice declined to comment on the delay Sunday.
But David Uhlmann, a University of Michigan law professor who headed the Justice Department's Environmental Crimes Section for many years, said a settlement with BP and one of the other parties makes a government settlement much more likely.
"There is no way the judge would have agreed to a delay unless a significant settlement was within reach," Mr. Uhlmann said.
Transocean Inc., the owner of the drilling rig used at the Deepwater Horizon site, has been battling with BP over liability. Brian Kennedy, a spokesman for Transocean, said the delay "does not change the facts of the case. Transocean is fully prepared for trial."
Among those represented by the lawyers involved in the talks with BP are people who didn't like the offers made to them through a BP-funded claims system set up outside the courts, as well as plaintiffs who had their claims denied in the claims process.
BP has paid some $6.1 billion to more than 200,000 individuals and businesses through the Gulf Coast Claims Facility. An additional $400 million in payments have been offered by the fund but haven't yet been completed.