Woods also said that oil supplies would likely remain plentiful despite an extended cut.
Oil prices have continued to grow driven by the joint announcement made by Saudi Arabia and Russian Federation to extend crude supply cuts until the end of March 2018.
Earlier this month, Saudi Arabia's oil minister indicated that his country would back an extension to the cap.
The current agreement that started on 1 January effectively cut oil production by Opec and non-Opec countries by nearly 1.8 million barrels per day (bpd), but that has not helped crude futures move above the $50 per barrel levels.
Oil prices continue growing.
The Organisation of Petroleum Exporting Countries (OPEC) will be meeting on May 25, 2017 in Vienna, Austria to discuss the possibility of an extension of the historic oil deal, struck in 2016.
Brent crude, the global benchmark, had risen $1.50 to $52.34 a barrel by 1152 GMT and traded intraday at $52.52, the highest since April 24.More news: Times Square crash victim was 18 year old Michigan woman
Surging U.S. output has raised concern that the cuts are failing to reduce a glut. USA drillers added nine rigs targeting crude, bringing the total to 712, the most since April 2015, Baker Hughes Inc. said Friday.
ST PETERSBURG, Russia The main goal of proposed extension of oil output cuts deal is to bring the global commercial oil inventories down to 5-year average and stabilize the market, Russian Energy Minister Alexander Novak said on Tuesday.
"There are no fast solutions to end this situation, and the only solution possible is to let oil prices work their way" to clear the oversupply, Al-Husseini said from the Saudi city of Dhahran.
The supply cut has helped prices recover from a low of $26 a barrel early a year ago. Oil has surrendered about half its gains since the producers' accord to cut output late a year ago.
The first source familiar with Iranian thinking said it was necessary to support prices to ensure there is enough investment in supplies to avoid shortages in future, echoing a view often expressed by Saudi Arabia. Sloup says it could surpass that if buoyed by higher prices.
USA production is now forecast to average about 9.31 million bpd this year - a level reached already, according to government figures.
Crude futures were building on their overnight gains Tuesday morning in Asia, amid expectations that USA data this week will show draws in crude and refined product inventories for the week ended May 12.