Brent crude settled at $73.79 a barrel, up $1.56, or 2.2%, while U.S. West Texas Intermediate (WTI) settled at $71.91 a barrel, rising $1.61, or 2.3%.

"The death of demand was greatly exaggerated," said Phil Flynn, senior analyst at Price Futures Group in Chicago. "Demand is not going away, so we're back looking at a very tight market."

Members of the Organization of the Petroleum Exporting Countries and other producers including Russia, collectively known as OPEC+, agreed this week on a deal to boost oil supply by 400,000 barrels per day from August to December to cool prices and meet growing demand.

But as demand was still set to outstrip supply in the second half of the year, Morgan Stanley forecast that global benchmark Brent will trade in the mid to high-$70s per barrel for the remainder of 2021.

"In the end, the global GDP (gross domestic product) recovery will likely remain on track, inventory data continues to be encouraging, our balances show tightness in H2 and we expect OPEC to remain cohesive," it said.

Russia may start the process of banning gasoline exports next week if fuel prices on domestic exchanges stay at current levels, Energy Minister Nikolai Shulginov said, further signalling tighter oil supplies ahead.

Crude inventories in the United States, the world's top oil consumer, rose unexpectedly by 2.1 million barrels last week to 439.7 million barrels, up for the first time since May, U.S. Energy Information Administration data showed. [EIA/S]

Inventories at the Cushing, Oklahoma crude storage hub and delivery point for WTI, however, has plunged for six continuous weeks, and hit their lowest since January 2020 last week.

"Supplies fell further by 1.3 million barrels to the lowest level since early last year, theoretically offering support to the WTI curve," said Jim Ritterbusch of Ritterbusch and Associates.

Gasoline and diesel demand, according to EIA figures, also jumped last week.

Barclays analysts also expected a faster-than-expected draw in global oil inventories to pre-pandemic levels, prompting the bank to raise its 2021 oil price forecast by $3 to $5 to average $69 a barrel.

(Additional reporting by Ron Bousso in London and Jessica Jaganathan in SingaporeEditing by Marguerita Choy and Kirsten Donovan)

By Laila Kearney