NEW ORLEANS — With billions of dollars at stake, the trial to figure out how much more BP and other companies should pay for the nation’s worst offshore oil spill began today with the federal government saying the oil giant was mostly to blame for a disaster caused by putting profits ahead of safety.

Justice Department attorney Mike Underhill said BP PLC, which leased the rig and owned the blown-out Macondo well, said the disaster resulted from the London-based company’s “culture of corporate recklessness.”

“The evidence will show that BP put profits before people, profits before safety and profits before the environment,” Underhill said during opening statements.

Eleven workers died when the rig exploded April 20, 2010, and millions of gallons of oil spilled into the Gulf of Mexico. U.S. District Judge Carl Barbier is hearing the case without a jury and — barring a settlement — will decide months from now how much more money BP and other companies involved in the ill-fated drilling project owe for their roles in the environmental catastrophe.

“Despite BP’s attempts to shift the blame to other parties,” Underhill said, “by far the primary fault for this disaster belongs to BP.”

Attorney Jim Roy, who represents individuals and businesses hurt by the spill, said BP executives applied “huge financial pressure” on its drilling managers to “cut costs and rush the job.” The project was more than $50 million over budget and behind schedule at the time of the blowout, Roy said.

“BP repeatedly chose speed over safety,” Roy said, quoting from a report by an expert who may testify later.