Oil prices fell for a third-straight session as slowing rig count cuts added to losses that had been mounting because of historically high U.S. supplies.

The U.S. Energy Information Administration reported on Thursday that U.S. crude inventories reached another record last week, a sign that cheap prices haven’t begun to affect production yet. The rising supplies led to the oil market’s first weekly loss in nearly a month.

Rig counts kept falling in new data released Friday, but the 37-rig decline was less than half of that registered a week ago. That could be a bearish sign that production won’t fall to balance the market as quickly as some had hoped. The day’s losses mounted on the news.

Light, sweet crude for March delivery, the U.S. benchmark, settled down 82 cents, or 1.6%, to $50.34 a barrel on The New York Mercantile Exchange. The March contract expired at the end of Friday’s trading. The more actively traded April contract settled down $1.02 cents, or 2%, at $50.81 a barrel.

The front-month April contract for Brent crude settled up 1 cent, or 0.02%, at $60.22 a barrel on London’s ICE Futures exchange.

Dean Hazelcorn, trader at Coquest Inc. in Dallas, said he was surprised prices didn’t move more on the news. Randall Collum, an analyst at Genscape Inc., had said earlier in the day that the rig-count cuts tallied by Baker Hughes Inc. likely would slow in the weeks to come.

“I have to think it met exactly expectations,” Mr. Hazelcorn said. The market “has been so docile.”

Expiration likely sapped some of the volatility, he added. Others said growing stocks were still pushing a selloff. The EIA said oil inventories grew by 7.7 million barrels last week to 426 million barrels, the highest level for this time of year for at least 80 years.

“It’s just crazy, these numbers and how it just keeps coming,” said Peter Donovan, broker for Liquidity Energy in New York. “Until you see it slowing down, there’s always going to be this downward pressure on the market.”

Oil futures had received a boost from petroleum products, which are surging in part because of weather in the U.S., brokers said. Cold weather boosts demand for heating fuel like diesel, and subzero and subfreezing temperatures are going to be common for most of the country through next week, meteorologists said. Two East Coast refiners are also having problems Friday, including frozen equipment that has kept ships from unloading at Delta’s Trainer refinery, Reuters reported Friday.

March diesel skyrocketed to a two-month high, settling up 11.8 cents, or 6%, at $2.1118 a gallon. Nymex reformulated gasoline blendstock for March—the benchmark gasoline contract—rose 1.5% to $1.6407 a gallon.

Mr. Collum and others warned that it could be months before the market reduces its oversupply, which analysts estimate at about 2 million barrels a day. The EIA reported on Thursday that U.S. crude production was running at a multiyear high of 9.3 million barrels a day.

Other major producers also appear to be ramping up output. Saudi Arabia could be producing as much as 10 million barrels of oil a day, PIRA Energy Group said in a report this week. The Kingdom’s output has kept steady in recent months at about 9.7 million barrels a day, according to Organization of the Petroleum Exporting Countries data.

Saudi-led OPEC decided not to cut output last year despite the price rout in an apparent attempt to defend its market share against the booming U.S. shale industry.

On Friday, financial markets were focused on the impasse between Greece and its creditors over a new financing deal for the country. Eurozone finance ministers are due to meet later Friday to hammer out a deal to avert a potential Greek exit from the eurozone, a prospect that has rattled markets in recent weeks. Tepid oil demand from Europe’s struggling economies contributed to the oil price crash last year.

—Georgi Kantchev Nicole Friedman and Tommy Stubbington contributed to this article.

Write to Timothy Puko at tim.puko@wsj.com

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