Oil prices steadied on Friday, but fell for the week on a stronger U.S. dollar and fears that an economic slowdown would weaken crude demand.

Brent crude futures settled at $96.72 a barrel, gaining 13 cents. U.S. West Texas Intermediate (WTI) crude ended 27 cents higher at $90.77. Both benchmarks fell about 1.5 percent on the week.

Oil briefly jumped in volatile trade on comments by the U.S. Richmond Federal Reserve President Thomas Barkin, who said the drive to raise rates also needs to be balanced with the impact of rate hikes on the economy. But crude pared its gains as investor concerns about upcoming rate hikes settled back in.

Strength in the U.S. dollar hit a five-week high, which also capped crude's gains as it makes oil more expensive for buyers in other currencies.

"Although the oil complex has been able to shrug off a strong dollar on any given session, extended strong dollar trends will pose a major headwind against sustainable oil price gains," Jim Ritterbusch, president of oil trading advisory firm Ritterbusch and Associates, said in a note.

In a sign of easing oil supply tightness, the price gap between prompt and second-month Brent futures has narrowed by about $5 a barrel since the end of July to under $1. The spread for WTI has shrunk to a 39-cent premium from a nearly $2 premium in late July.

Supplies could tighten again when European buyers start seeking alternative supplies to replace Russian oil ahead of European Union (EU) sanctions that take effect from December 5.

"We calculate the EU will need to replace 1.2 million barrels per day of seaborne Russian crude imports with crude from other regions," consultancy FGE said in a note.

Data from earlier this week showed U.S. crude inventories fell sharply as the world's top producer exported a record 5 million barrels per day last week, with oil companies finding demand from European nations looking to replace Russian crude.

(Source: Reuters with edits)