Prices have eased a little and market fundamentals have improved in recent weeks, but concerns remain due to unplanned supply outages, international political tension over Iran and limited spare production capacity, she said.
"Prices remain very high," van der Hoeven told an industry event in Australia in a video presentation. "High prices pose a real threat to the economic recovery."
The IEA advises 28 industrialized nations on energy policy.
Earlier, Minister of Petroleum and Mineral Resources Ali Al-Naimi said Saudi Arabia wants an oil price of around $100 a barrel and would like to see global inventories rise before demand picks up in the second half of the year.
"We want a price around $100, that's what we want," Al-Naimi told reporters in Australia. "A $100 price is great."
Saudi Arabia is working at bringing Brent crude prices to that level, he added. The Kingdom, OPEC's biggest producer, said it pumped 10.1 million bpd in April, its highest for more than 30 years, as it bid to meet growing demand and curb oil prices.
Prices have stayed high in 2012 due to concern about disruption to global supply from US and European sanctions aimed at hurting Iran's crude export revenues and forcing Tehran to halt its nuclear program.
Al-Naimi said last week that producers were pumping enough to deal with the impact of the sanctions on the oil market.
He reiterated on Sunday that producers were pumping 1.3 million barrels per day (bpd) to 1.5 million bpd above demand, which is helping to build inventory.
"That should give comfort to consumers," he said.
Inventories are at the equivalent of around 58 days of demand, but Saudi Arabia would like to see stockpiles build more ready for the seasonal increase in fuel consumption in the second half of the year, Al-Naimi said.
"It should be a little bit higher, because you are going into the third and fourth quarter, and demand will be higher as usual," he said.
