BP's chief financial officer Brian Gilvary said that factors that reduced the company's first-quarter cash flow - increases in working capital and payments related to the oil spill from the Macondo well in the Gulf of Mexico - would fade later in the year.
In the first quarter, BP bought back 18 million shares worth $120 million.
The company was forced to take a surprise $1.7 billion charge to net income in the fourth quarter because the cases that did remain were among the largest and most complex.
He added: "Our safe and reliable operations and strong financial delivery have continued into 2018".
But the group continued to count the cost of its 2010 Deepwater Horizon tragedy in the Gulf of Mexico, with another $1.6bn (£1.2bn) forked out in the first quarter - including $1.2bn (£873m) for the final payment of its 2012 settlement with the Department of Justice.
Bob Dudley, chief executive, hailed a "strong set of results", which were the oil major's best quarterly performance in three years. Shares rose 1.2 per cent to 544.5 pence at 8.19 am in London. It is still paying on it, and it will continue to pay for several more years, but as oil prices improve so has BP's outlook for the future.
First-quarter results in the sector have been a mixed bag, with Royal Dutch Shell and Exxon Mobil falling short of forecasts, while results from Chevron and Total were stronger than expected.
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Earnings after taxation, or bottom-line net profit, jumped to $2.5 billion (2.1 billion euros) in the three months to the end of March from a year earlier, BP said in a results statement.
Underlying replacement cost profit, a key measure used by analysts to assess BP's profitability, came in ahead of expectations at $2.6bn, but investors could be spooked by a rise in debt from $38.6bn to $40bn.
The company's production, meanwhile, rose 6% in the first quarter compared with a year ago.
It has so far cost the group more than 65 billion United States dollars (£48 billion), and although BP has all the major settlements now under its belt, it still has a few smaller legal bills to pay.
The surge in revenue led BP last October to become the first European oil major to resume share buybacks in order to offset the dilutive effect of so-called scrip dividend, where shareholders can opt to receive dividends via cash or shares.
The further hit from the spill in the first quarter sent the firm's debt levels rising to 40 billion USA dollars (£29 billion) from 38.6 billion U.S. dollars (£28.2 billion) a year ago.