BP has revealed that there is just $300m (£196.7m) left in its Gulf of Mexico oil spill compensation fund as it vowed to fight "false and fictitious" claims related to the disaster.

The oil company took another $1.4bn in provisions related to the Deepwater Horizon disaster in the second quarter, nearly exhausting a $20bn fund set aside to deal with damages payments. It said claims that exceeded the remaining $300m in future periods would be taken against company income.

BP increased its overall provision for the rig explosion which killed 11 people in 2010 by $200m to $42.4bn, but the bill for the clean-up, fines and compensation could ultimately be significantly higher.

"There are a significant number of business economic loss claims which have been received but have not yet been processed, and further claims are likely to be received," the company said.

BP's chief executive, Bob Dudley, said the company was prepared for long-haul legal battles and is appealing against compensation claims worth more than $1bn which he described as "absurd".

"We stepped up to obligations following that terrible accident, a lot of people died. I think our intention was very clear to pay legitimate victims of the spill … [but] people we believe made no losses as a result of the spill are getting paid for it. And we intend to fight this vigorously. We are fighting this aggressively because we have a duty to our shareholders, but also because it's the simply the right and principled thing to do."

In a warning to vexatious claimants, he added: "As we continue to fight these absurd outcomes, and as the likelihood of extended litigation on other matters increases as a result, we want everyone to know that we are digging in and are well-prepared for the long haul on legal matters."

He said that last week alone plaintiffs' attorneys themselves had submitted claims averaging $1.5m per firm, and said it would fight those larger claims that it believed to be illegitimate.

Dudley also said that while BP was happy to pay out for legitimate claims from hotels, restaurants and shops along the coastline, it was appealing against claims from larger businesses such as construction companies and farms that were claiming economic loss despite being located "far away from the coast".

He said the type and scale of some of the claims BP was facing was a clear sign that class action suits in the US were "somewhat out of control". He added: "The original intent of class action seems to have been morphed into something that I think is very unhealthy for business in the United States. What's happening to us [in Louisiana] is a very big example which is why it's worth everyone's attention."

He made the comments as BP revealed that underlying profit in the second quarter fell to $2.7bn from $3.6bn a year earlier, sharply below analyst forecasts of $3.4bn. The company blamed lower oil prices compared with a year earlier, an "unusually high" tax rate because of a stronger dollar and lower income from Russia.

It was the first full quarter to reflect BP's 19.75% stake in Russia's Rosneft, which was boosted in size earlier this year when BP sold its shareholding in TNK-BP to Rosneft. The company's share of Rosneft's earnings was $218m.

BP said it had passed its $38bn divestment target to help create a Deepwater Horizon compensation fund, leaving it with "a stronger set of assets".

The FTSE 100 company said it expected third-quarter production to be lower than in the second quarter because of planned activity and repairs in the North Sea, planned maintenance in Alaska and the continued impact of asset sales.

Dudley said: "The results show strong underlying pre-tax performance from BP's businesses. We are seeing growth in ­production from new high-margin projects and are making good progress in exploration and project delivery.

"Completion of our operational milestones confirms our confidence in delivering our commitment to materially increase operating cash flow in 2014."