It added that supply cuts this year by the Organization of the Petroleum Exporting Countries (OPEC) and non-affiliated allies like Russian Federation - known as the OPEC+ alliance - aimed at tightening oil markets were also supporting crude prices. U.S. West Texas Intermediate (WTI) crude futures rose 55 cents, or 1 percent, to $57.34 a barrel.
Mr. Falih said the group was unlikely to change its output policy in April and if required would make adjustments in June.
Brent crude futures rose 9 cents, or 0.1 percent, to settle at $66.67 a barrel.
The Organization of the Petroleum Exporting Countries (OPEC) and its allies such as Russian Federation - known as the OPEC+ alliance - will meet in Vienna on April 17-18, with another gathering scheduled for June 25-26. "But, barring this, I think we will just be kicking the can forward", Mr Falih said.
Oil rose to around $67 a barrel on Tuesday, supported by Saudi Arabia's plan for further voluntary supply curbs in April and by a cut in oil exports from Venezuela due to a power outage.
But the Paris-based International Energy Agency predicted a surge in USA production, which would see its exports exceed Russia's and near Saudi Arabia's by 2024.
"The United States emerges as a significant oil exporter", said Fatih Birol, IEA executive director, during a press conference at an industry summit in Houston.
"The IEA continues to see no peak in oil demand, as petrochemicals and jet fuel remain the key drivers of growth, particularly in the United States and Asia, more than offsetting a slowdown in gasoline due to efficiency gains and electric cars", the IEA said.
Despite the gains, commodities markets were somewhat held back after USA 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.
"Brent prices have struggled to push firmly above $65 per barrel in part because a strong U.S. dollar remains a major headwind for commodity prices".
He also said that along with China and the US, India's expanding economy was driving global oil demand growth.
"(Despite economic headwinds), we still see Brent prices averaging $70 per barrel this year and expect WTI to lag, averaging $59 per barrel in 2019", said Bank of America Merrill Lynch.