Both contracts are on track for a 2%-3% drop this week but still far from a low of $60.47 hit two weeks ago.
Downward pressure has been exerted by the decision of the Organization of the Petroleum Exporting Countries (OPEC) and its allies, known as OPEC+, to increase supplies by 2 million barrels per day between May and July.
Analysts expect global oil inventories to continue to fall, but predict fuel demand will accelerate in the second half of the year as the global economic recovery gathers steam.
“A lot of destocking is going on, so we are well into the rebalancing process,” said Energy Aspects analyst Virendra Chauhan.
Physical markets will still need to pick up before prices and inter-month spreads can rally, he added.
For all the optimism, renewed lockdowns in some parts of the world and problems with vaccination programmes could threaten the oil demand picture.
Stephen Innes, chief global markets strategist at Axi, said oil prices are expected to trade in a range between $60 and $70 as investors weigh these factors.
“Oil is currently in a wait and see mode, with market participants looking at the vaccination pace to understand when oil demand will recover further and at nuclear talks in Vienna to see when more Iranian barrels might come back,” said UBS commodity analyst Giovanni Staunovo.
Talks to bring Iran and the United States fully back into the 2015 nuclear deal are making progress, delegates said on Friday, but Iranian officials indicated disagrement with Washington over which sanctions it must lift.
“If a fulsome framework can be crafted in the coming weeks, significant quantities of Iranian oil will likely hit the market in H2 2021,” RBC Capital analyst Helima Croft said in a note this week.