International benchmark Brent crude was trading at $44.91 at 1302 GMT on Friday, posting a 3.8% rise from trade on Monday at 0630 GMT when it traded at $43.25 per barrel.
American benchmark West Texas Intermediate traded at $41.78 at the same time on Friday relative to $39.91 a barrel on Monday.
Iraq declared that it would make an additional cut in its oil output of about 400,000 barrels a day in August to offset its overproduction under the OPEC+ supply reduction agreement over the previous term. Under the agreement the country settled on its output of 1.06 million bpd.
Saudi Arabia, de facto OPEC leader and key driver of supply cuts for OPEC+, also said it would further limit its supply to support prices.
Despite the further cuts made by the two Arab nations to counter the overproduction under the OPEC+ supply reduction deal, concerns over the effectiveness of the steps against the second wave of coronavirus limit the outlook for global oil demand.
On Thursday, Energy Information Administration (EIA) announced US commercial crude oil inventories fell by 7.4 million barrels for the week ending July 31, the data showed.
Meanwhile, oil rates were also boosted by a weakening dollar, which makes oil relatively cheaper for foreign-currency holders.
According to the latest data from Johns Hopkins University the number of COVID-19 cases worldwide has now exceeded 19 million. As the US leads with nearly 4.8 million cases, Brazil has over 2.9 million, and India follows with more than 2 million cases.