BP has started the "static kill" of its leaking Gulf of Mexico oil well, a step towards permanently sealing it.
Specially formulated mud is being pumped in from the top, forcing oil back down into the well.
After the procedure - which could last up to two-and-a-half days - the top of the well could be filled with cement.
The US government estimates the well leaked 4.9 million barrels of oil before being capped last month, with only 800,000 barrels being captured.
Pressure in the well dropped rapidly in the first hour-and-a-half of the work, indicating that good progress was being made.
The well ruptured after an explosion on a drilling rig in April which killed 11 workers.
The new assessment of the leak is higher than previous estimates. The figure will be crucial in calculating the environmental damage done, as well as the money to be paid by BP.
The BP spill is greater than the 1979 Ixtoc I leak in the Gulf of Mexico, which gushed 3.3 million barrels.
Only the intentional release of an estimated eight million barrels of oil into the Gulf by Iraqi troops during the Gulf War in 1991 was greater in recent decades.
During the "static kill" procedure, BP engineers will pump enough drilling mud into the well to counter the pressure from the oil pushing out of the reservoir below the seabed, BP senior vice-president Kent Wells told reporters.
"We're so early in the process there's no way for me to give you any early indication. The only thing I would say is the injectivity test went well and so that gives us the encouragement," said Mr Wells late on Tuesday.
If that goes well, the company could top off the well with cement to seal it.
Meanwhile, work on a relief well - currently 100ft (30m) away from intersecting with the damaged well - will continue, incident commander Admiral Thad Allen said.
The relief well will reach the damaged well some time between 11 and 15 August. When that is complete, BP may pump cement from the relief well into the bottom of the damaged well, in a procedure called a "bottom kill".
The well initially leaked about 62,000 barrels of oil per day, higher than any previous estimate of the flow. But as the reservoir of oil became depleted, the flow slowed to about 53,000 barrels per day.
The flow ended on 15 July, when BP closed a new cap it had put on the well.
Last week, BP reported a record $17bn (£11bn) loss, having set aside $32bn to cover the costs of the spill.