LONDON (MarketWatch) — British oil giant BP PLC remains committed to deepwater drilling in the Gulf of Mexico but will take a step back and review its equipment and procedures in the area before attempting to jump back in, Chief Executive Robert Dudley said Tuesday.

As he presided over his first set of quarterly results, Dudley told reporters in London that although the U.S. government earlier this month lifted the ban on deepwater drilling imposed in the wake of the Macondo incident, the actual regulatory steps required before companies can resume drilling in the area have yet to be detailed.

He expects the industry to get back to work in the area in the course of 2011 and said BP(BP.) BP, -2.09% would not be the first one to jump back in.

“It would not be sensible for us to raise our hand and rush with the first permit application,” he said.

Instead, BP plans to thoroughly review its equipment but also its safety and operational procedures in the region. Once it has a better sense of how long obtaining a new permit may take, the company will decide what to do with the rigs it currently has sitting idle in the region.

“We’re waiting to see the pace at which things progress in the Gulf before making a decision,” Dudley said.

Rebuilding reputation to take time

The executive, who took over from Tony Hayward one month ago, insisted in his presentation on the need to rebuild trust, particularly in the U.S., after the “traumatic” incident.

The midterm elections taking place Tuesday in the U.S. — which could shift control of Congress to Republicans — will not change the fact that rebuilding BP’s reputation is “going to take time,” Dudley said.

At the height of the spill, President Barack Obama repeatedly clashed with BP management over its handling of the crisis.

Dudley’s relationship with the U.S. government and other parties involved has appeared smoother than that of his predecessor. He is also well acquainted with important local players after spending a significant chunk of the summer overseeing the cleanup operations on the coast.

He is not, however, planning to return to the affected area in the near future, he admitted Tuesday, stressing that the bulk of the cleanup effort has now been accomplished.

Not grossly negligent

BP reported a 67% drop in third-quarter profit as it took a further $7.7 billion charge related to the spill, bringing its total best estimate of the price tag of the incident to $39.9 billion. Read more about BP’s earnings

That forecast, however, is based on BP’s conviction that it will not be found “grossly negligent,” and Dudley said the company isn’t making contingency plans in case it is found to have been.

Still, he said it would be “imprudent” to categorically rule out further charges.