By early afternoon in Europe, benchmark crude was up 15 cents at $88.58 a barrel in electronic trading on the New York Mercantile Exchange. The contract rose $1.33 to end at $88.43 in New York on Monday.
In London, Brent crude was up $1.10 at $104.03 a barrel on the ICE Futures exchange.
Oil was underpinned by expectations that U.S. and China will do more to prop up slowing economic growth. The two countries are the world's biggest and second-biggest crude consumers. As consumers spend more and the economy strengthens, demand for oil is likely to rise.
Some analysts believe Federal Reserve Chairman Ben Bernanke will talk about additional stimulus when addresses Congress on Tuesday and Wednesday.
Expectations of possible Chinese stimulus measures rose after Premier Wen Jiabao's weekend promise of tax breaks and other aid to struggling small businesses. China's second-quarter growth fell to a three-year low of 7.6 percent but analysts said a rebound might be in sight.
"The latest statements ... by Chinese Prime Minister Wen Jiabao, coupled with renewed speculation that Fed chairman Bernanke may announce the possibility of further quantitative easing of U.S. monetary policy at his testimony before the U.S. Congress today, are currently giving buoyancy to crude oil prices," said analysts at Commerzbank in Frankfurt. "Apart from the supply risks and the hope of further stimulus measures, there are currently only few arguments which would justify the latest rise in the price of crude."
The main supply risk at the moment is judged to be the rising tension between the United States and Iran.
Oil prices were boosted Monday after U.S. Navy gunners aboard a refueling ship opened fire on a small boat racing toward them in broad daylight near Dubai. One person was killed and three were injured. All were Indian nationals and India's ambassador to the United Arab Emirates said Tuesday that the fishermen aboard the boat said they were given no warning before being fired upon.
The incident took place not far from approaches to the Strait of Hormuz, a key route for oil tankers which Iran has threatened to block in response to Western sanctions against Tehran's oil exports.
Investors will also be monitoring fresh information on U.S. stockpiles of crude and refined products.
Data for the week ending July 13 is expected to show a draw of 1.4 million barrels in crude oil stocks and a build of 700,000 barrels in gasoline stocks, according to a survey of analysts by Platts, the energy information arm of McGraw-Hill Cos.
The American Petroleum Institute will release its report on oil stocks later Tuesday, while the report from the Energy Department's Energy Information Administration — the market benchmark — will be out on Wednesday.
In other futures trading, heating oil was up 2.3 cents at $2.8480 a gallon and gasoline rose 2.18 cents to $2.8765 a gallon. Natural gas was down 1 cent at $2.79 per 1,000 cubic feet.