Chief executive Bob Dudley said he expects crude prices to recover towards the end of this year as producers halt work on oil fields and fuel demand stays robust.
The 80 per cent fall in first quarter profits beat analysts’ expectations.
The firm maintained its dividend and said it could cut capital spending further.
Joe Rundle, head of trading at ETX Capital, said: “Overall it’s a good set of figures as it looks like BP is getting costs under control.”
The British oil company, the first major to report on one of the weakest quarters, lowered its 2016 spending target to £12bn, from £12bn to £13bn, and said the target could fall to £10bn to £12bn next year if oil prices remain weak.
The cost reductions mean the oil producer is forecasting it can balance its books at an oil price of $50-55 a barrel in 2017, down from $60 previously.
“Market fundamentals continue to suggest that the combination of robust demand and weak supply growth will move global oil markets closer into balance by the end of the year,” said Mr Dudley.
The BP CEO suffered an embarrassing shareholder revolt earlier this month when investors rejected his £13.7m remuneration package.
Almost 60 per cent of shareholders rejected BP’s remuneration report.
Faced with the worst downturn in the oil sector in at least three decades, BP reduced its capital spending three times in 2015 to £13bn, slashed nearly 10 per cent of its 80,000 strong workforce and sharply lowered costs.
BP slipped to its biggest annual loss last year as a result of lower oil prices, costs related to the settlement of a deadly 2010 Gulf of Mexico oil spill and huge write downs.
BP’s first quarter underlying replacement cost profit, its definition of net income, was £365m, down from £1.8bn a year earlier but beating forecasts for a loss of £96m.
It said 2017 cash costs will be £5bn lower than for 2014.
BP’s current total charge for the Gulf of Mexico oil spill has risen to £39bn after an additional payment of £630m in the first quarter, which was outside a settlement reached last year.
The group is the first oil major to reveal the financial impact of record-low oil prices in the first quarter and will be closely followed by peers Total, Statoil and Eni later this week and Shell on May 4.
BP’s refining and trading segment, known as downstream, once again came to the rescue with a quarterly profit of £1.2bn, offsetting a £513m loss in oil and gas production.
BP maintained its dividend at 7p per ordinary share.
The figures show trading has improved markedly since a dire end to 2015.
The oil price crash left BP nursing its largest annual loss for at least 20 years, slumping into the red by £3.6bn in 2015, surpassing even the mammoth losses seen in the wake of the Deepwater Horizon explosion and oil spill in the Gulf of Mexico in 2010.
The cost of crude has bounced back in recent weeks, now trading at around $45 a barrel, while BP is also beginning to see the benefits of swingeing cost-cutting actions.
Mr Dudley said: “Despite the challenging environment, we are driving towards our near-term goal of rebalancing BP’s cash flows.”
Mr Rundle at ETX Capital said that the results may “stick in the throat of some investors” in light of Mr Dudley’s pay deal.
“While this shows progress, it needs to do more to cut costs,” he said.