- The Saudi energy minister raised the prospect of prolonged output restraint once an OPEC-led supply-cutting pact ends.
- Iraqi pro-government paramilitaries launched an offensive against Kurdish troops on Tuesday near the Turkish frontier.
- Analysts expect U.S. crude inventories to decline by 2.5 million barrels in the latest weekly supply reports.
Oil prices rose in volatile trade on Tuesday after top exporter Saudi Arabia said it was determined to end a supply glut, while prices also drew support from forecasts of a further drop in U.S. crude inventories.
The Saudi energy minister said the focus remained on reducing oil stocks in industrialized countries to their five-year average and raised the prospect of prolonged output restraint once an OPEC-led supply-cutting pact ends.
The oil market has been concerned that, once the supply deal expires, producers will ramp up shipments again and cause prices to fall.
"When we get closer to that (five-year average) we will decide how we smoothly exit the current arrangement, maybe go to a different arrangement to keep supply and demand closely balanced so we don't have a return to higher inventories," the minister, Khalid al-Falih, told Reuters.
Brent crude, the global benchmark, rose 99 cents, or 1.7 percent, to $58.36 a barrel by 2:30 p.m. ET (1830 GMT). It fell as low as $57.04 earlier in the session.
U.S. crude for December delivery ended Tuesday's session up 57 cents, or 1.1 percent, at $52.47, having touched a session low of $51.55.
Analysts said it was difficult to pin the sharp gyrations in the oil market on Tuesday on any one headline.
"There's these headlines coming out of the Saudi conference," said Again Capital founding partner John Kilduff, referring to the Future Investment Initiative summit in Riyadh. "Every now and then, they succeed at saying something positive."
"They have the megaphone. They're using it," he told CNBC.
Technical analysts believe Brent needs to breach the $58.54-$58.88 level to break out higher, according to Tom Kloza, global head of energy analysis at Oil Price Information Service. The breakout range for WTI is $52.37 to $52.86, he said.
"Unless we get through that, everything is kind of a tease right now," he told CNBC.
Oil was down earlier in the session as crude flows through Iraq's northern pipeline to Ceyhan in Turkey rose further. Pumping along the pipeline rose to 300,000 bpd on Tuesday, a shipping source said. Output fell from 600,000 bpd last week when Iraqi forces retook control of oilfields from Kurdish fighters.
Iraqi pro-government paramilitaries launched an offensive against Kurdish troops on Tuesday near the Turkish frontier, pushing towards a strategic border crossing and oil export pipeline hub that Baghdad says must come under its control.
The Kurds held a referendum on independence last month that Baghdad called illegal. Baghdad responded by seizing back the city of Kirkuk, the oil-producing areas around it, and other territory that the Kurds had captured from Islamic State.
The disruption to exports from Iraq, the second-largest producer in OPEC, has helped support the market and should give the group's already high compliance with the cutback agreement a boost in October.
OPEC, plus Russia and nine other producers, have cut oil output by about 1.8 million barrels per day (bpd) since January. The pact runs to March 2018 and they are considering extending it.
Analysts expect U.S. crude inventories to decline by 2.5 million barrels in the latest weekly supply reports. Gasoline and distillate stockpiles also probably fell by at least 1.5 million barrels, a preliminary Reuters poll showed on Monday.
Industry group American Petroleum Institute (API) is scheduled to release its data at 4:30 p.m. ET (2030 GMT) on Tuesday. The government's Energy Information Administration reports on Wednesday.
— CNBC's Tom DiChristopher contributed to this report.