Oil prices not going up soon: IEA director

The International Energy Agency does not see oil prices bouncing back to a higher level very soon, the organization's executive director told CNBC's "Squawk Alley" on Thursday.

The IEA cut its forecast for oil demand in 2015 to 93.3 million barrels per day last week, shaving 230,000 bpd of growth from an earlier projection.

The organization sees demand growth slowing next year in the former Soviet Union area, China and a number of oil-producing nations, said the IEA's Maria van der Hoeven. At the same time, the organization believes the market is "well supplied," she said.

The market has begun to respond as oil producers announce that they will postpone a number of investments, she said.

Chevron has put a plan to drill for oil in the Beaufort Sea in Canada's Arctic on indefinite hold, while Marathon Oil cut its capital expenditure budget for next year by about 20 percent.

Canadian oil producers also deepened cuts in 2015 spending, as Husky Energy, MEG Energy and Penn West Petroleum joined those hacking back capital budgets in response to tumbling crude prices.

Brent Crude and WTI surged about 3 percent in early morning trading, but pared gains to fall roughly $1 below their session open by midday.

—Reuters contributed to this story.