Oil prices reached fresh multi-year highs on Friday, closing out a third straight week of gains on an improved outlook for worldwide demand as rising COVID-19 vaccination rates help lift pandemic curbs.

Brent crude futures settled at $72.69 a barrel, rising by 17 cents after reaching their highest since May 2019. For the week, Brent was up by 1 percent.

U.S. West Texas Intermediate (WTI) crude futures settled at $70.91 a barrel, up by 62 cents, settling at their highest since October 2018. WTI was up by 1.9 percent on the week.

"Demand is coming back faster than supply and we're going to need more supply to meet that demand," said Phil Flynn, senior analyst at Price Futures Group in Chicago.

The International Energy Agency (IEA) said in its monthly report that the Organization of the Petroleum Exporting Countries and allies, known as OPEC+, would need to boost output to meet demand set to recover to pre-pandemic levels by the end of 2022.

"OPEC+ needs to open the taps to keep the world oil markets adequately supplied," the Paris-based energy watchdog said.

It said that rising demand and countries' short-term policies were at odds with the IEA's call to end new oil, gas and coal funding.

"In 2022 there is scope for the 24-member OPEC+ group, led by Saudi Arabia and Russia, to ramp up crude supply by 1.4 million barrels per day (bpd) above its July 2021-March 2022 target," the IEA said.

U.S. investment bank Goldman Sachs said it expects Brent crude prices to reach $80 per barrel this summer as vaccine rollouts boost global economic activity. 

"The rollout of the vaccine in North America as well as Europe is helping to restore demand at the same time that OPEC+ has reigned in production," helping propel oil prices, said Andy Lipow of Lipow Oil Associates in Houston.

Data showing road traffic returning to pre-COVID-19 levels in North America and most of Europe was encouraging, ANZ Research analysts said in a note.

"Even the jet fuel market is showing signs of improvement, with flights in Europe rising 17 percent over the past two weeks, according to Eurocontrol," ANZ analysts said.

In an indication of future supply, U.S. oil rigs rose by six to 365 this week to their highest since April 2020, energy services firm Baker Hughes Co. said in its weekly report. It was the biggest weekly increase of oil rigs in a month.