NEW ORLEANS — A BP executive who led the company’s efforts to halt its massive 2010 oil spill in the Gulf of Mexico testified Tuesday that his decisions were guided by the principle that they shouldn’t do anything that could make the crisis worse.

James Dupree, BP’s first witness for the second phase of a trial over the disaster, said his teams worked simultaneously on several strategies for killing the well that blew out in April 2010.

Dupree said the company scrapped plans to employ a capping strategy in mid-May because the equipment wasn’t ready. He also said he was concerned that it could jeopardize other efforts to seal the well.

“We were very intent not to make the situation worse,” said Dupree, who was made a regional president for BP after the spill was stopped.

But BP’s trial adversaries have argued that the company could have stopped the spill much earlier than July 15 if it had used that capping strategy.

Earlier Tuesday, an employee of the company that owned the doomed Deepwater Horizon drilling rig testified that he was surprised when BP scrapped the capping strategy his team had devised and never heard an explanation for the decision.

“We were so close. We had come a long way,” said Robert Turlak, Transocean’s manager of subsea engineering and well control systems.

During the first few weeks after the spill, engineers focused on two methods for stopping the flow of oil and capping the well was one option. The other, called “top kill,” involved pumping drilling mud and other material into the Deepwater Horizon rig’s blowout preventer.

BP ultimately used a capping stack to stop the spill July 15 after several other methods failed.

Turlak’s team was working on a strategy that was called “BOP-on-BOP” because it lowered a second blowout preventer on top of the rig’s failed one. He called it the “obvious solution” and said to use in early June.

But BP concluded it wasn’t a viable option because it could have made the situation worse and hampered other strategies if it failed. BP said the capping stack that later sealed the well was specifically designed to land on the well system above the blowout preventer.

BP employed the “top kill” method in May 2010, but it didn’t stop the flow of oil. The company says its adversaries have ignored evidence that the “BOP-on-BOP” option wasn’t approved or ready for safe installation before “top kill.”

The trial’s second phase opened Monday with claims that BP ignored decades of warnings about the risks of a deep-water blowout and withheld crucial information about the size of the spill.