BP, on the back foot all week answering tough questions on the Gulf spill and its safety record in general, said it "strongly disagrees" with Anadarko's claims.
Anadarko's shares rose by 2.2 per cent in after-hours trading following Hackett's statement.
In contrast, moments after Anadarko's statement, credit rating agency Moody's cut BP's rating to junk level, citing potential liability from the spill.
Earlier in the day Moody's cut by three notches its rating on BP debt, which is trading around junk levels.
Scrambling for cash
BP is scrambling to line up resources to pay for a $20bn damage claims fund demanded by Barack Obama, the US president.
BP was seeking $1bn in loans from seven different banks, the Reuters news agency said, while US broadcaster CNBC said the energy giant was hoping to raise $5bn with a bond.
BP said on June 4 that it had $5bn in cash in addition to $5.25bn in undrawn committed bank lines, and $5.25bn in committed standby bank lines.
Carl-Henric Svanberg, BP's chairman, told broadcaster Sky News Television on Friday that his company had "strong underlying performance - strong cash flow, strong operations".
But Kenneth Feinberg, the man picked by Obama to oversee the $20bn compensation fund, told CBS News on Friday that the amount may not be enough to meet all legitimate claims.
"No one knows for sure yet, but the president made clear, and as I understand it BP went along, that if $20bn is not enough, there will be additional funds provided," he said.
BP's shares are down 26 per cent so far in June, their worst month since the October 1987 stock market crash.
Investors appeared unimpressed by the performance of Tony Hayward, BP's chief executive, at a US congressional hearing on Thursday.
Legislators accused him of being evasive and of failing to take responsibility for the spill.
Hayward has been sharply criticised for saying he wanted his "life back" after coming under intense pressure as the face of BP throughout the crisis.
On Friday he appeared to be relieved of those duties, with chairman Svanberg saying Hayward would hand over day-to-day handling of the spill to the company's managing director, Robert Dudley.
Svanberg himself was criticised for earlier in the week describing those hurt by the giant oil spill as "small people", a remark for which he later apologised.
On a more positive note, the US Coast Guard admiral leading the US government's relief effort, said BP had increased the amount of oil it was siphoning off from the damaged well to 25,000 barrels (3.97 million litres) on Thursday - the largest amount of oil collected from the gusher yet.
|BP collected 25,000 barrels on Thursday, but the well could be spewing 60,000 [Reuters]
On Wednesday, it siphoned off 18,600 barrels.
But putting that figure in context, Admiral Thad Allen said 35,000 to 60,000 barrels per day was gushing from the well, as the crisis entered its 60th day.
BP hopes a pair of relief wells now being drilled will halt the leak in August. The aim is for one or both relief wells to intersect with the leaking well at its bottom to pump in heavy drilling fluids and cement to seal it.
The first relief well is within 61 metres of the side of the blown well, said Kent Wells, BP's senior vice-president of exploration and production.
But it must be drilled down farther before it can intersect with the blown well.
The well was damaged following an explosion on the Deepwater Horizon drilling platform on April 20 and its sinking two days later.
Eleven workers were killed in the blast and the ensuing giant spill has been described as the worst environmental disaster in US history.