Washington (CNN) -- A top White House aide and the managing director of oil giant BP provided differing versions Sunday for who provided the initial inaccurate estimates of the size of the Gulf of Mexico oil spill.

Robert Dudley, the BP official who appeared on CNN's "State of the Union" and other talk shows, said early estimates that 5,000 barrels (210,000 gallons) were leaking into the ocean each day came from government satellite imaging, rather than BP's figures.

An updated estimate issued last week by a government-led team put the leak at 12,000-19,000 barrels (504,000 to 798,000 gallons) a day, more than double the initial figure.

"The best way to measure those early rates or estimate those early rates were from satellite data, not BP data," Dudley said on the CBS program "Face the Nation."

Not true, countered Carol Browner, the assistant on energy and climate change to President Obama, who spoke to the NBC program "Meet the Press" and the CBS show.

"The very, very first estimates came from BP," Browner said on the CBS program. "They had the footage of the plume. The government then did satellite imagery and we realized that those estimates were not accurate."

Browner noted that BP had a "vested financial interest" in downplaying the size of the leak.

"They will ultimately pay a fine based on those rates," Browner said. "That's why we brought in an independent team. We did not include BP in the estimates that were made available this week."

Rep. Ed Markey of Massachusetts, who heads the House Energy and Environment subcommittee, agreed that the company "had a stake in low-balling the number right from the very beginning."

"I think that they were either lying or they were incompetent," Markey said on the CBS program. Noting that BP has consistently provided information that proved to be wrong, Markey said he had "no confidence whatsoever in BP."

"I think they do not know what they are doing," Markey said, adding: "I don't think that people should really believe what BP is saying in terms of the likelihood of anything that they're doing is going to turn out as they're predicting."

Browner emphasized steps the government has taken to oversee BP's efforts to stop the leak, noting the administration ordered the company to begin digging two relief wells intended to eventually stop the leak instead of a single one proposed by BP.

In addition, she said, it was government scientists led by Energy Secretary Steven Chu who recommended that BP halt the so-called "top kill" effort to pump heavy mud down the well to try to plug the leak.

"It was that group of people yesterday who looked at the information we had gotten from 'top kill' and realized that it was too dangerous to continue to proceed to put pressure down into that well, that things could happen that would make the situation worse," Browner said.

Dudley told CNN that BP was "disappointed the oil is going to flow for a while and we're going to redouble our efforts to keep it off the beaches."

The top kill effort failed because "there was just too much flow" of oil and gas coming out of the well, Dudley said.

He detailed a plan to cut a new opening in equipment from which the oil is leaking to try to lower a cap over it and pipe up most of the leak. A similar previous effort failed, and Dudley said steps would be taken to prevent the problems from the first attempt.

"Our objective is to contain a majority of the oil and gas," Dudley said, adding that cutting the new opening was unlikely to increase the amount of oil leaking out before the cap is placed.

Browner, however, said on the CBS program that an increase of up to 20 percent was possible. And Markey, on the same show, contended that BP "has been making it up as they go along the whole way.

"They do not know for sure what the result is going to be of anything which they are doing," Markey said.