"Output and employment gaps remain in many countries, particularly in emerging-market and developing economies where vaccination rates are low," the report said.
The OECD lowered its growth outlook for the United States, from 6.9 to 6.0 per cent this year. The US Congressional Budget Office has forecast 6.7 per cent growth for the world's top economy.
The Delta variant hit the US economy harder in the second quarter "but it is picking up again very strongly," the OECD's chief economist, Laurence Boone, said at a news conference.
The OECD's eurozone forecast was raised by one point to 5.3 per cent, though the outlook varied within the single-currency bloc, with higher growth now expected in France, Italy and Spain while Germany was not performing as well.
The growth prospects of Argentina, Brazil, Mexico, South Africa, South Korea and Turkey have also improved, while those of Australia, Britain, Japan and Russia were lowered.
The forecast for China, the world's second biggest economy and a driver of global growth, remained unchanged at 8.5 per cent.
The impact of the Delta variant of the coronavirus has "so far been relatively mild" in countries with high vaccination rates, but it has lowered the momentum elsewhere and added pressures to global supply chains and costs, the OECD said.
"Sizeable uncertainty remains," the report said, warning that slow progress in vaccination drives and the spread of virus mutations would lead to a weaker recovery and larger job losses.
"What worries us even more is that many emerging markets with the exception of China are still far behind advanced ones for vaccination programme levels," Boone said.
"The situation is even worse in low income countries."
Earlier this month, United Nations chief Antonio Guterres expressed disappointment that vaccine-manufacturing nations have been unable to ramp up production toward the goal of vaccinating some 70 per cent of the world population by the first half of 2022.