Crude oil benchmarks ended a volatile quarter with their biggest losses in history, as both U.S. and Brent futures were hammered throughout March on the global economic freeze due to the coronavirus pandemic and the eruption of a price war between Russia and Saudi Arabia.

Both benchmarks lost roughly two-thirds of their value in the quarter, with March's declines of about 55% accounting for the lion's share of the losses.

WTI crude posted a modest 2% gain on March 31, while Brent ended slightly lower.

Global fuel demand has been sharply cut by travel restrictions due to the coronavirus pandemic. Forecasters at major merchants and banks see demand slumping by 20% to 30% in April, and for weak consumption to linger for several months.

WTI settled 39 cents higher at $20.48 per barrel. The U.S. benchmark plunged 54% during March and 66% for the first quarter, the biggest such declines since the contract's inception in 1983.

May Brent crude futures ended 2 cents lower at $22.74 a barrel ahead of expiration. The international benchmark fell 66% in the first quarter and 55% in March, the biggest quarterly and monthly percentage declines on record.

The more-active June contract settled 7 cents lower at $26.35 a barrel.

Prices fell in post-settlement trade after data from industry group the American Petroleum Institute showed U.S. crude inventories rose by 10.5 million barrels last week, far exceeding forecasts for a 4 million barrel build.

Oil drew some early buying after U.S. President Donald Trump and Russian counterpart Vladimir Putin agreed to talks on stabilizing energy markets.

Markets have been in turmoil for more than three weeks. Early this month, prices fell sharply after Saudi Arabia and Russia were unable to come to an agreement to curb supply. Prices fell even more as demand fell during the worsening coronavirus pandemic. More than 800,000 people have been infected and more than 39,000 have died.

It remained unclear whether Trump and Putin's efforts will come to fruition. Saudi Arabia and other members of OPEC were unable to come to an agreement on March 31 to meet in April.

Saudi Arabia, de facto leader of OPEC, remains at loggerheads with Russia, which had allied with OPEC to curb output for more than three years beginning in late 2016. The Saudis plan to boost oil exports to 10.6 million barrels per day (bbl/d) from May on lower domestic consumption.

Weakness in futures markets has been surpassed by the physical markets, where cargoes are selling at single digits in key markets like Canada, Mexico and Europe, reflecting expectations for the coming collapse in demand that will strand barrels of oil.

"COVID has taken the oil market hostage," said Michael Tran, managing director of energy strategy at RBC Capital Markets in New York.

"The unprecedented pace of demand destruction has forced the hand of refineries, on a global level, to issue run cuts, leaving barrels from the U.S. to the North Sea, to Asia searching, often unsuccessfully, for homes."

Fuel demand is expected to fall sharply in coming months, with Trafigura's chief economist predicting a 30% falloff in demand. Worldwide aviation is basically shut down, and motorists are staying off the roads.

"It's just a matter of time before we see the producers be forced by the crude gatherers to cut as one cannot 'gather' crude when there are no buyers or tanks to store it in," said Scott Shelton, energy specialist at United ICAP.

U.S. crude output fell to 12.7 million bbl/d in January from 12.8 million bbl/d in December, the U.S. Energy Information Administration (EIA) said in a monthly report on March 31.

That was the first time since July 2019 that U.S. crude output has declined two months in a row. Goldman Sachs anticipates that U.S. supply will fall by roughly 1.4 million bbl/d by the third quarter of 2021 to deal with falling demand.

A Reuters survey of 40 analysts forecast Brent crude prices would average $38.76 a barrel in 2020, 36% lower than the $60.63 forecast in a February survey.