Brent crude futures rose 68 cents to settle at $61.32 a barrel. US West Texas Intermediate (WTI) crude futures rose 20 cents to settle at $52.31 a barrel.
Boosting oil prices, Wall Street's main indexes hit a one-month high. Crude futures sometimes track equity markets.
Futures drew support from a supply cut agreement from the Organization of the Petroleum Exporting Countries (OPEC) and major non-OPEC producer Russia. The group agreed in December to cut combined oil output by 1.2 million barrels per day from January.
Russia's deputy energy minister said the country will reach its oil output target reduction in April.
"The market is consolidating. To see what our next driver is, we're going to watch to see if the cuts are working, if the members that agreed to them are adhering to them," said Gene McGillian, director of market research at Tradition Energy.
Despite the output cuts, rising crude oil production in the United States could pressure prices. The US Energy Information Administration (EIA) said crude production rose last week to a record 11.9 million barrels per day, as crude exports jumped close to record highs near 3 million bpd.
US fuel stockpiles rose more than forecast and were up for the fourth straight week, EIA data showed.
US crude output is expected to grow this year to a record beyond 12 million bpd, with the country turning into a net crude exporter in late 2020, the EIA said on Tuesday.
Gasoline stockpiles rose 7.5 million barrels, far exceeding analysts' expectations in a Reuters poll for a 2.8 million-barrel gain. At 255.6 million barrels, gasoline stocks were at the highest weekly level since February of 2017.
Distillate stockpiles, which include diesel and heating oil, increased 3 million barrels, versus expectations for a 1.6 million-barrel rise, the data showed.
Crude inventories fell 2.7 million barrels, more than double forecasts.
"Any bullish sentiment from the crude draw has been vanquished by emphatic builds to the products," said Matthew Smith, director of commodity research at ClipperData.
Mounting signs of an economic slowdown across the world may also keep oil prices in check.
White House estimates showed on Tuesday that the US economy is taking a larger-than-expected hit from a partial government shutdown.
The outlook for the global economy darkened further after Britain's parliament on Tuesday shot down Prime Minister Theresa May's deal to leave the European Union.
China this week reported poor December trade data. China's central bank on Wednesday made its biggest daily net cash injection via reverse repo operations on record, in efforts oil markets will watch closely.