US crude oil futures settled at $58.26 a barrel, rising $1.39 cents, or 2.44 percent.
The supply growth is a positive thing in the IEA's view, as oil demand around the world could increase by up to 1.2 million barrels per day over the next five years.
An oil pump is seen operating in the Permian Basin near Midland, Texas, U.S. on May 3, 2017.
Brent was at $67.14 a barrel at 1320 GMT, up 47 cents or 0.7 percent.
"With the refiners starting to slowly come out of maintenance, OPEC cuts starting to kick in, and Venezuelan supplies, you're probably now looking at a future with more draws in the coming weeks", said Phil Flynn, analyst at Price Futures Group in Chicago.
Crude oil prices rose marginally on Monday, driven by comments from Saudi Arabian oil minister, Khalid al-Falih, that an end to the Organisation of Petroleum Exporting Countries (OPEC)-led supply cuts was unlikely before June. In particular, Saudi Arabia's oil production in February fell to 10.136 million bpd, a Saudi industry source told Reuters on Friday, down from 10.24 million bpd in January.
"US oil consumption [growth] previous year was about a half-million barrels per day, and as such it was the highest in all the countries around", Birol noted on Monday.
Oil prices have also received support from supply cuts led by the Organization of the Petroleum Exporting Countries and allies including Russian Federation.
Saudi Energy Minister Khalid al-Falih told Reuters two days ago that it would be too early to change a production curb pact agreed by the Organisation of Petroleum Exporting Countries (OPEC) and its allies, which includes Russian Federation, another major producer, before June.
Exports from Venezuela's main oil terminal have been stranded as its worst blackout on record has left parts of the country without power for roughly a week. U.S. crude shipments are projected to stand at 8.93 million barrels a day in five years - just 0.59 million less that Riyadh, and 0.24 million barrels more than Moscow.
According to an annual five-year outlook report by the International Energy Agency, the United States became the world's top oil producer in 2018, and is set to become the world's biggest oil exporter over the next five years.
Despite the gains, commodities markets were somewhat held back after US employment data raised concerns that an economic slowdown in Asia and Europe was spilling into the United States, where growth has so far still been healthy.