By Edward McAllister
Saudi Arabia, the world's biggest oil exporter, has reduced exports by around 900,000 barrels per day from a peak in August, one source estimated.
U.S. crude rose $5.01 to $68.92 a barrel by 11:17 a.m. EST. London Brent crude was up $4.27 at $64.75 a barrel.
"The petroleum markets have rebounded from lower overnight levels on a trio of supportive factors: a weaker U.S. dollar, a push to the upside in global equity markets and market talk that Saudi Arabia may have already cut crude oil production," Tim Evans, analyst at Citi Futures Perspective, said in a research note.
U.S. stocks climbed further on Tuesday as the presidential election got under way, while investors picked up shares trading around five-year lows amid further signs of easing in global credit markets.
Saudi Arabia's supply cut helps to remove doubts about whether the world's top exporter would comply quickly with a 1.5 million barrel per day output cut agreed by the Organization of the Petroleum Exporting Countries in Vienna last month.
Other OPEC members have also cut back.
The United Arab Emirates has reduced its production to around 2.3 million barrels per day from around 2.5 million bpd, a top state oil company official said on Tuesday.
Algeria is reducing its oil output by 71,000 bpd in line with OPEC's supply-cut decision, the Algerian official news agency APS said on Tuesday, quoting the country's Energy and Mining Ministry.
Qatar has cut exports to Asia by about 40,000 barrels per day (bpd) from this month, Energy Minister Abdullah al-Attiyah told Reuters.
Earlier, the market had fallen more than a dollar, pressured partly by expectations oil refiners would have to cut output because of weak demand for fuel.
Crude oil has plummeted from a record above $147 a barrel in July as the credit crisis in the global banking sector has started to hit the wider economy. This has already damped fuel consumption in the United States, the world's top oil consumer, and other major consumer nations.
U.S. auto sales plunged 32 percent in October to lows not seen in a quarter century, while U.S. factory activity -- a barometer for future oil demand -- fell to its lowest level in 26 years.
U.S. factory orders fell steeply for the second month in a row during September.
(Additional reporting by Jane Merriman and Joe Brock in London; editing by Jim Marshall)