LONDON—Oil prices rose modestly on Wednesday but were under pressure ahead of key U.S. supply data as investors remain wary of the continuing Greek debt negotiations.

Brent crude for August delivery rose 0.1% to $64.50 a barrel on London's ICE Futures exchange. On the New York Mercantile Exchange, West Texas Intermediate futures for July were trading up 0.1 % at $61.05 a barrel.

The American Petroleum Institute, an industry group, reported a larger-than-expected 3.2 million-barrel decline in U.S. inventories last week. The data also showed a 2.0 million-barrel drop at the key trading hub of Cushing, Okla.

The U.S. Energy Information Administration will release its official inventory data later on Wednesday. Analysts polled by The Wall Street Journal expect a 2.3 million-barrel drop.

Investors are still looking for strong signs that the market is in the process of rebalancing, said Dominick Chirichella of Energy Market Analysis. "So far the only sign has been a steady destocking of crude oil inventories in the U.S. for the last two months as refiner demand remains robust heading into the summer driving season."

The EIA's report will also be scrutinized for its U.S. oil production estimate. Despite the significant drop in oil drilling rigs since last year, U.S. producers kept pumping crude at a multi-decade high of around 9.6 million barrels a day.

According to the Kuwait Official News Agency, the country's Oil Minister Ali al-Omair said that oil prices are likely to rise further because of the fall in stockpiles, fewer drilling rigs and the improved global economic growth.

"We have reached a stage where a drop in oil prices is unlikely," he said, reported the news agency.

Meanwhile, officials hope eurozone finance ministers on Wednesday can sign off on a policy package agreed to by Greece and the institutions overseeing its bailout. But significant divisions remain between Athens and its creditors

Failure to clinch a deal could put Greece on the road to bankruptcy and exit from the common currency area. A Greek default could hurt European oil demand, analysts said.

"Tremors in the financial markets can create big waves in the oil markets making a fool of even the best thought out analysis on the direction of oil prices," said David Hufton of PVM brokerage.

Nymex reformulated gasoline blendstock for July—the benchmark gasoline contract—rose 0.7% to $2.0906 a gallon, while ICE gasoil for July changed hands at $587.75 a metric ton, up $3.50 from Tuesday's settlement.

Summer Said in Dubai contributed to this article.

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

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