Brent crude futures were up 85 cents, or 0.9%, to $94.81 a barrel by 0827 GMT, after rising by as much as $1.03. U.S. West Texas Intermediate crude futures climbed $1.06, or 1.17%, to $91.45 after gaining as much as $1.24, Reuters reported.

Industry data released on Tuesday showed U.S. crude oil stockpiles rose last week by about 1.6 million barrels, against analysts' expectations for a drop of about 300,000 barrels.

However, markets continued to worry about U.S. crude stockpiles at the key Cushing, Oklahoma, storage hub falling below minimum operating levels.

Further drawdowns at Cushing, the delivery point for U.S. crude futures, could also provide new upward pressure on oil markets as it would compound supply tightness stemming from supply cuts by the Organization of the Petroleum Exporting Countries and allies, together called OPEC+.

"Oil prices are overall relatively strong amid the current tightening of supply," said CMC Markets analyst Leon Li, however the price support from Russia and Saudi Arabia's supply cuts may be limited through the year-end.

"(Economic) data from countries in Europe and the United States have recently weakened ... Oil prices in October may show a volatile trend as a whole. It is unlikely to exceed $100 in the short term, but it is expected to be strong."

U.S. government data on oil inventories is expected at 10:30 a.m. (1430 GMT).

Russia last week imposed a temporary ban on gasoline and diesel exports to most countries to stabilise the domestic market, and though it later softened restrictions, these could put upward pressure on crude oil demand from refineries.

Meanwhile, a "soft landing" for the U.S. economy is more likely than not, Minneapolis Federal Reserve Bank President Neel Kashkari said on Tuesday, but there is also a 40% chance that the Fed will need to raise interest rates "meaningfully" to beat inflation.

The Bank of England has concluded its tightening cycle and will likely keep the Bank Rate at 5.25% until at least July, a Reuters poll of economists showed, although a minority said it would hike rates again this year.

Higher interest rates increase borrowing costs, which could slow economic growth and reduce oil demand.