* No need to worry about market glut, IEA says
* Joins EIA, OPEC in raising demand growth estimate
* OECD oil inventories drop sharply in third quarter (Adds Brent price, OPEC and EIA forecasts)
LONDON, Feb 13 (Reuters) - Stronger-than-expected demand has drained oil inventories to the lowest level since 2008, tightening the market and defying predictions of a glut, the West's energy watchdog said on Thursday.
The International Energy Agency (IEA) said oil inventories in the developed world plummeted by 1.5 million barrels per day (bpd) in the last three months of 2013, the steepest quarterly decline since 1999.
The IEA, which advises most of the largest energy-consuming countries on energy policy, becomes the third major forecaster this week to predict higher oil use as economic growth picks up in Europe and the United States.
"Far from drowning in oil, markets have had to dig deeply into inventories to meet unexpectedly strong demand," the IEA said in its monthly oil market report.
The IEA raised its forecast for global oil demand growth this year by 50,000 bpd to 1.3 million bpd.
That was boosted by a rebound in demand in North America and Europe after several years of declining consumption.
The Paris-based agency increased its estimate of the demand for oil from the Organization of the Petroleum Exporting Countries (OPEC) from last month's report by 100,000 bpd to 29.6 million bpd .
"Demand has been stronger than expected, and we're operating with low stock levels right now, which has been supportive for prices," Antoine Halff, head of the IEA's oil industry and markets division, told Reuters.
"Demand for OPEC crude looks stronger."
Both OPEC and the U.S. Energy Information Administration raised their forecasts for 2014 demand in monthly reports this week.
Growing oil production in North America had led some to predict international crude prices would fall in 2014, after averaging around $110 a barrel in each of the past three years.
But robust demand and supply problems in a number of OPEC countries have kept prices supported, the IEA said.
While output from Libya recovered in January to 500,000 bpd, Iraqi output fell by 140,000 bpd to 2.99 million bpd, the IEA said, and warned that exports from Libya were likely to continue to be constrained by political unrest in the country.
Output in Saudi Arabia, OPEC's largest producer, fell by 60,000 bpd in January to 9.76 million bpd, the IEA said.
Halff said demand for OPEC crude oil could be even stronger in the coming months as companies moved to rebuild oil inventories to a more comfortable level.
The IEA kept its estimate for supply growth from countries outside of OPEC unchanged from last month, forecasting an increase of 1.7 million bpd this year.
"We're going into a period of lower demand as refineries start maintenance after the winter," Halff said.
"We need to rebuild stocks."
Benchmark Brent crude oil prices were down about 0.5 percent on Thursday at $108.24 a barrel, slipping after hitting a month-high of $109.75 at the start of the week. (Reporting by Christopher Johnson and David Sheppard; editing by Jason Neely)