The British oil giant now has just $300m (£200m) left in the fund, and the deadline to file a business economic loss claim among Gulf coast businesses - which make up the bulk of claims - is not until April 2014.
BP has said claims beyond what the fund can pay will be taken straight off future profits.
The firm revealed the extra cost in its second quarter results, which missed forecasts due to the lagging effect of tax in Russia where the price of Urals crude was weaker.
It also said it was due to the tax effects of a stronger dollar on a basket of currencies.
Adjusted net profit for the three months was $2.712bn (£1.35bn) compared with expectations of $3.410bn and $3.6bn (£2.5bn) a year ago.
Of the extra $1.4bn of spill costs - which come on top of a $500m (£300m) cost in the first half - some $900m is for extra claims, while about $500m is for the administration costs of the claims administrator.
It also faces a resumption of its trial on civil charges in September.
BP remains locked in a legal battle over the compensation payouts, some of which it claims are spurious, and has increased its overall provision for the spill to $42.4bn (£27.7bn) from $42.2bn.
It set up a hotline for whistleblowers to give tip-offs about fraudulent claims.
The oil giant alleges that the handling of the settlement has sparked a "feeding frenzy" and is allowing businesses from the area to claim for "non-existent, artificially calculated losses".
The blow-out of the Deepwater Horizon well off the Louisiana coast in 2010 claimed 11 lives and damaged fishing, tourism and wildlife habitats, forcing BP to agree a multi-billion compensation deal in April 2012.
But it has warned in court filings that it will be "irreparably harmed" unless the compensation system is reformed, saying the cash drain could put its dividend at risk and make it vulnerable to a takeover.
However, chief executive Bob Dudley said the latest results showed there had a been a strong underlying pre-tax performance from its businesses, with growth in production from new projects and good progress in exploration.
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