Crude prices settled more than half a percent higher on June 26 as some traders found bargains after last week's seven-month lows, but rising crude supply in the US and other countries limited gains.
Brent for August settlement gained as much as 62 United States cents, or 1.4 per cent, to US$46.16 a barrel on the London-based ICE Futures Europe exchange.
Stocks at the Cushing, Oklahoma, delivery hub for USA crude futures fell 297,000 barrels, the EIA said.
Oil had recovered some ground over the past week after falling almost 20 per cent since mid-May, but a report by the American Petroleum Institute (API) showed that U.S. crude inventories rose by 851,000 barrels in the week to June 23 to 509.5 million, compared with analysts' expectations for a decrease of 2.6 million barrels.
Gasoline inventories recorded a draw of 0.9 million barrels on the week with a 0.8% annual increase while distillate recorded a draw of 0.2 million barrels with a year-on-year increase of 1.2%.
However, the latest oil market report from OPEC showed that production increased by 336,000 barrels in May, thanks largely to two exempted countries, Libya and Nigeria.
Exports have fallen from the highs of February, averaging 775,000 b/d during the four weeks ending on June 16, but up from the same time previous year when they were at 489,000 b/d, according to EIA data.
Both benchmarks were up over 5 percent since June 21 when Brent fell to a seven-month low of $44.35 and WTI fell to a 10-month low of $42.05.
The main reason behind the unchecked drop in crude oil prices is that the supply of oil in circulation is more than the demand.
Oil prices rose for a fourth consecutive session on Tuesday boosted by a weaker USA dollar and investors covering short positions, but worries over persistent oversupply capped gains. Crude has lost more than 20% of its value over the past six months.
His comments were taken negatively by some market participants, who say that rapidly increasing USA production at a time of stubborn oversupply will end up hurting shale producers. US crude inventories remain stubbornly high, more than 100 million bbl above the five-year seasonal average, according to data from the EIA. But BP's (BP) U.S. -listed shares rose 0.5% to 35.125, and Royal Dutch Shell (RDSA) was up 0.8% to 53.67.