LONDON—Oil prices rose in a volatile session Thursday as investors brace themselves for key U.S. oil supply data.

Brent crude for July delivery recently rose 0.7% to $62.48 a barrel on London's ICE Futures exchange. On the New York Mercantile Exchange, West Texas Intermediate futures for July were trading up 0.3% at $57.67 a barrel.

Late Wednesday, the American Petroleum Institute, an industry group, reported a surprise 1.3-million-barrel rise in U.S. crude stockpiles for last week.

The more closely watched data by the U.S. Energy Information Administration is due later, and markets expect weekly supplies to have decreased by 1.1 million barrels, according to analysts polled by The Wall Street Journal.

"Consensus [for the EIA report] is small draws in crude, gasoline and distillates inventories, expect volatility if the report differs from expectations," said Michael Poulsen, oil analyst at Global Risk Management.

The EIA will also release U.S. weekly oil production estimates. Signs that low oil prices are starting to affect U.S. oil production and inventories are among the key factors that supported bullish price sentiment and helped oil prices rally in recent weeks.

Uncertainty surrounding nuclear negotiations with Iran is also fueling bullish sentiment as an expected increase in the country's oil exports hinges on the outcome of the talks.

Keeping the original June 30 deadline for a final deal on the Iranian nuclear program looks increasingly difficult and there still seems to be hurdles to overcome between the parties, Mr. Poulsen said.

"Most likely, the deadline will be postponed to some time in July. This makes the likelihood of Iranian oil flooding into the market this year less likely," he said.

Meanwhile, market participants are turning their focus on next week's meeting by the Organization of the Petroleum Exporting Countries. OPEC is meeting at its Vienna headquarters on June 5 and is widely expected to maintain its production target as it did at its last meeting in November despite falling prices and the global glut of oil.

"While OPEC again is facing continued oversupply, lower oil prices do appear to be having the intended effect of reducing investment by non-OPEC producers," analysts at UBS said in a report. "Thus, we see no reason for the Gulf members to shift their position and hence no change from OPEC."

Nymex reformulated gasoline blendstock for June—the benchmark gasoline contract—rose 1% to $1.9655 a gallon, while ICE gasoil for June changed hands at $574.00 a metric ton, down $2.25 from Wednesday's settlement.

Eric Yep in Singapore contributed to this article.

Write to Georgi Kantchev at georgi.kantchev@wsj.com

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