Drilling rigs are parked up in the Cromarty Firth near Invergordon, Scotland, Britain January 27, 2015.
Brent crude futures gained 22 cents, or 0.3 percent, to $66.80 a barrel by 1:08 p.m. EDT (1708 GMT).
High drilling activity past year resulted in a more than two million barrels per day rise in production, to 12.1 million bpd reached this February, making the United States the world's biggest producer of crude oil ahead of Russian Federation and Saudi Arabia.
April West Texas Intermediate crude, +0.82 per cent rose 86 cents, or 1.5 per cent, to $56.93 a barrel on the New York Mercantile Exchange, after prices rose 0.5 per cent last week, according to Dow Jones Market Data.
The US will rival Saudi Arabia as the world's biggest exporter of oil products within five years as shale output achieves explosive growth, catapulting America into strategic dominance of the global energy system.
Prices of the barrel of the American benchmark for the sweet light crude oil remain firm in the first half of the week and are now targeting yearly peaks in the mid-$57.00s.
Despite this, oil markets have generally been supported this year by ongoing supply cuts led by the Organization of the Petroleum Exporting Countries (OPEC) and some non-affiliated allies like Russian Federation - known as the OPEC+ alliance.
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Saudi Arabia, seeking to drain a supply glut and support prices, plans in April to keep its oil output well below the level required of it as part of an OPEC-led supply cutting deal, a Saudi official confirmed on Monday.
India has raised concerns about the rising price of crude oil during a meeting with Minister of Energy, Industry and Mineral Resources of Saudi Arabia and Chairman of Saudi Aramco, Khalid A Al-Falih.
Sources recently said the most likely scenario is that the current supply cuts will be extended in June but much depends on the extent of United States sanctions on OPEC members Iran and Venezuela.
Markets have been further tightened by the implementation of USA sanctions against oil exports from OPEC-members Iran and Venezuela.
Export of crude from Venezuela goes down due to massive power outage. "The EIA report reined some of that in, and the report was supportive in that respect", said John Kilduff, a partner at Again Capital LLC in NY.
In the near term, the latest reports on United States inventories are expected to show a rise in crude stocks.
The slowdown in drilling points to more timid output growth going forward, but because the overall drilling level remains relatively high despite the recent decline, many analysts still expect US crude output to rise above 13 million bpd soon.