NEW YORK--Oil futures climbed to a near-three-week high Thursday on continued supply drawdowns at a key storage hub and signs of improving U.S. demand.

Light, sweet crude for May delivery settled up $1.02, or 1%, at $101.28 a barrel on the New York Mercantile Exchange, the highest settlement price since March 7. Brent crude on the ICE futures exchange rose 80 cents, or 0.8%, to $107.83 a barrel, its highest level since March 14.

Supplies in Cushing, Okla., a main U.S. storage hub where the Nymex contract is priced, fell for the eighth straight week last week, the U.S. Energy Information Administration said Wednesday. Cushing stocks are at their lowest level since January 2012.

A storage glut has built up in Cushing as U.S. oil production rapidly increased without sufficient transportation channels to connect the crude to existing refineries. The bottleneck kept the price of West Texas Intermediate, the U.S. oil benchmark, below that of Brent crude oil, the international benchmark, in recent years.

A new pipeline opened in January connecting Cushing to Gulf Coast refineries and lifting the price of U.S. oil compared to Brent. The price gap between the two contracts fell to less than $6 a barrel at the beginning of March and settled today at $6.55 a barrel. As recently as late November, the benchmark U.S. contract was trading nearly $20 a barrel below Brent.

"WTI continues to move higher in reaction to lower and lower Cushing crude-oil inventories," said Andy Lipow, president of Lipow Oil Associates in Houston.

However, demand for crude oil has fallen in recent weeks as refineries have closed units to perform seasonal maintenance. Nationwide, crude-oil supplies have risen for 10 straight weeks. And on the Gulf Coast, supplies hit an all-time high last week, according to the EIA.

"Cushing has been drained, and all that inventory is moving to the Gulf Coast," Mr. Lipow said.

Still, Mr. Lipow said he expects Cushing inventories to continue to fall for several more weeks.

"Until we completely fill up the Gulf Coast and we start backing oil into Cushing because there's no place to put it (on the Gulf Coast), we continue to see this strength" in prices, he said.

Futures were also supported by positive U.S. economic data Thursday morning, which could indicate improving demand in the top oil-consuming nation.

The number of people filing new claims for jobless benefits fell to a seasonally adjusted 311,000 last week, the Labor Department said. Economists had expected 325,000 new claims for the week.

Also on Thursday, the Commerce Department said U.S. gross domestic product rose at a 2.6% annual rate in the fourth quarter, higher than its previous calculation of 2.4% and just below economists' estimates of 2.7% growth.

Front-month April reformulated gasoline blendstock, or RBOB, settled up 3.37 cents, or 1.2%, to $2.9426 a gallon, the highest price since March 14. April diesel rose 2.83 cents, or 1%, to $2.9477 a gallon, its highest level since March 11.