Also, the production cuts made by OPEC countries made Dubai, an Asian benchmark, more expensive compared to the US counterpart.
Light sweet crude oil (WTI) futures gained 0.80 dollar or 1.58 percent to close at USD 51.51 a barrel at the New York-based commodity exchange NYMEX.
Traders said that slowly tightening market conditions were driving price rises, with the Organization of the Petroleum Exporting Countries (OPEC) leading an effort to cut output.
Brent crude, the Global benchmark for oil in the region, rose 54 cents to $54.71 per barrel.
But demand is picking up ahead of summer in key markets, including the United States, where analysts forecast industry data this week will show a fall in oil inventories.
"Should it confirm that US crude stocks did indeed fall for what would only be the second time this year, it will mark the start of a sustained tightening in USA crude supplies", said Stephen Brennock of oil broker PVM.
USA crude and oil product stocks probably fell last week after rising for two consecutive weeks, a Reuters survey showed. An outage at the largest U.K. North Sea oilfield lent support. Sinopec bought 1 million barrels of U.S. Mars Blend crude for loading in April, a person familiar with the matter said.
"These changes are a signal that the rebalancing is happening faster than many in the market believe".
Refinery crude runs rose by 203,000 barrels per day, EIA data showed.
Official data from the U.S. Energy Information Administration (EIA) is due on Wednesday morning.
Both climbed more than 1.5% during US trading Tuesday as the rebound continues following from March's selloff on worries about USA stockpiles and the resolve of countries to maintain production caps.
Oil prices had risen early after the American Petroleum Institute reported late on Tuesday that inventories fell by a more-than-expected 1.8-million barrels last week.
At the heart of the bloated US market is rising production, especially from shale drillers.
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The other two victims, Mohammed, 21, and Mustafa, 18, suffered minor injuries during the attack, the court was told. Daryl Davis and his sister, Danyelle, were slated to be released on bail along with the Potts, the girl's partner.