* Oil steadies around $71.50 after swinging wildly
* Crude prices down more than 17 percent since early May
* Coming Up: API inventory data on Tuesday
(Recasts, updates prices, market activity)
By Joshua Schneyer
NEW YORK, June 7 (Reuters) - Oil steadied on Monday as falling equities markets and a firming dollar were offset by expectations that U.S. crude stockpiles fell last week, modestly reducing brimming inventories.
Crude prices seesawed in thin trade, after falling by 3 percent earlier. Benchmark U.S. crude prices <CLc1> settled down 7 cents at $71.44 a barrel. ICE Brent crude for July <LCOc1> rose 3 cents to settle at $72.12 a barrel.
U.S. crude prices have declined by more than 17 percent since hitting a 19-month high above $87 a barrel in early May.
The Dow and S&P indexes fell in afternoon trade, after rising earlier, as a disappointing U.S. jobs report on Friday continued to weigh on investor sentiment.
Key U.S. stock indexes fell more than 3 percent on Friday. [
] Oil had fallen by more than 4 percent on Friday, on concern that a slow economic recovery could hurt fuel demand."Buyers are going to be extremely cautious after getting spanked in the market last week," said Peter Beutel, president of Cameron Hanover in Connecticut.
Oil industry tracker Baker Hughes said in a release on Monday that the number of U.S. offshore rigs declined in May to 49 from 53 in April. Analysts cited a ban on Gulf drilling following the Gulf oil spill.
"The decline in the rig count is important because people are starting to realize that the oil spill could bring declines in (U.S.) production," said Beutel.
Support for oil was seen in the start of the Atlantic hurricane season this week, which the top U.S. government weather agency has warned could be the most intense since 2005. [
]Energy analysts polled by Reuters expect data to show U.S. crude stocks fell by a modest 900,000 barrels last week as the country took fewer imports, but most also estimate that U.S. fuel stocks rose last week. [
]U.S. oil stocks data is due on Tuesday from the American Petroleum Institute and Wednesday from the government's Energy Information Administration.
A firming U.S. dollar and a late fall in equities proved bearish for energy traders. Many also stayed on the sidelines Monday, when thin-volume trade contributed to wide oil price swings.
The U.S. dollar gained late in the day against a basket of foreign currencies. <.DXY> A stronger dollar makes oil imports more expensive for European buyers and for consumers in Asia where demand is surging.
The chief of the International Monetary Fund downplayed on Monday market fears that Hungary could soon face a debt crisis like Greece.
"I see no reason to be ... concerned. They (the Hungarian government) will do what they have to do," IMF Managing Director Dominique Strauss-Kahn told reporters after talks with finance ministers from the 16-country euro zone. [
]The Hungarian government vowed to cut spending on Monday as it strove to repair damage from officials' comments last week about a possible Greece-style debt crisis. [
](Additional reporting by Edward McAllister and Gene Ramos in New York, David Sheppard in London, Fayen Yong in Perth and Alejandro Barbajosa in Singapore; Editing by David Gregorio)