BP has made an initial deposit of $3bn (£1.8bn) into a $20bn compensation fund for the oil spill, after completing talks with the US Department of Justice, according to BP officials.

The fund, called an escrow account, was set up by the oil giant to compensate victims of the Gulf of Mexico spill.

BP’s response has cost $6.1bn already.

Meanwhile, BP’s relief well will reach the damaged well by the end of the week and start the final “kill”, the government’s incident commander said.

An additional deposit of $2bn will be made in the fourth quarter by BP, with deposits of $1.25bn being deposited each of the following quarters until the $20bn has been paid in full.

“The purpose of the escrow account was to assure those adversely affected by the spill that we indeed intend to stand behind our commitment to them and to the American taxpayers,” BP’s incoming chief executive Bob Dudley said in a statement.

Associate Attorney General Tom Perrelli later said the justice department was “pleased that BP made an initial contribution and has taken an important step toward honouring its commitment to the president and the residents and business owners in the Gulf region”.

The account will be overseen by lawyer Kenneth Feinberg, who managed compensation claims made by victims of the 9/11 attacks.

The total $6.1bn cost of the spill includes the cost of the clean-up response, containment, relief well drilling and cementing-up of the damaged well.

The sum also includes grants to the Gulf states hit by the spill.

It also includes the $319m paid out in compensation to some of those affected by the spill.

Drilling continues

The announcement of BP’s deposit in the escrow account comes amid news that BP has made significant progress toward the final “kill”.

The relief well, which is closing in on the damaged well, is being drilled in sections of 20-30ft (6-9m), followed by “ranging runs” - tests to check it is on target.

“Yesterday we learned that the procedure to prevent any more oil from spilling with a cement plug appears to have succeeded”, said Barack Obama US president.

US Coast Guard Adm Thad Allen, the government’s incident commander, said the cement pushed through the top of the well last week had now hardened enough to allow workers to drill the final 100ft of the relief well.

When the relief well intersects the ruptured well, mud and cement will be pumped in and it will be permanently sealed.

President Barack Obama on Monday welcomed the news that operations in the Gulf appeared to be making progress.

“Yesterday we learned that the procedure to prevent any more oil from spilling with a cement plug appears to have succeeded,” he said.

“The final steps will be taken later in August when those relief wells are completed, but what is clear is that the battle to stop the oil from flowing into the Gulf is just about over.”

Oil stopped leaking into the Gulf of Mexico on 15 July for the first time since the explosion on the Deepwater Horizon oil rig in April. The blast killed 11 people.

An estimated 4.9 million barrels spilled from the damaged well in the 87 days from the beginning of the disaster until the leak was finally capped, the US government has said.

BP has yet to be drawn about what will happen to the oilfield after the damaged well is blocked. There is still a huge amount of oil in the reservoir deep under the seabed.