(Reuters) - Crude oil futures rose on Thursday, rebounding from the previous session's slump as investors fretted again about potential disruptions to Mideast oil supplies after talks between world powers and Iran over its nuclear program ended in Baghdad without an agreement.

After seeming conciliatory before the talks, Iran insisted on its right to nuclear fuel enrichment. Another meeting was set for June, suggesting that the situation remains fluid and prompting caution by oil investors. Trading volume was light and prices remained substantially below their highs for this year.

We are seeing a repeat of Iran's normal tactics -- it extends an olive branch but in talks later, nothing happens, and this is muddling the oil markets, said Kyle Cooper, managing partner at IAF Advisors in Houston, Texas.

For weeks, oil markets have been balancing risks of supply disruptions from Iran against the possibility that demand will slump due to a slowing global economic growth with the impact of the euro zone debt crisis weighing heavily.

Fears that Greece may leave the euro zone kept buyers cautious about bidding up oil prices too high. Weak economic data from China, Europe and the United States also fed jitters about the shaky global economy.

In China, factory output faltered in May, according to official data, as export orders fell to two-month lows, pointing to sluggish economic activity in the first half of the year and denting the outlook for oil demand.

The euro zone sunk further into the doldrums this month as new factory orders shriveled, forcing companies to run down backlogs and slash work forces, surveys showed.

Also worrying policymakers, the downturn that started in smaller members has spread to Germany and France, whose tepid growth had been keeping the troubled bloc afloat.

Demand for long-lasting U.S. manufactured goods rose less than expected in April while weekly jobless claims dipped only modestly, adding to worries about the economy of the world's largest oil consumer.

By 2:35 p.m. EDT, Brent July futures were up $1.09 at $106.65 a barrel. Brent touched a session high of $106.94 before weak Chinese and European economic data sparked selling. Then, it fell as low as $105.03, the lowest intraday price since December 20 -- down more than 18 percent from its 2012 high of $128.40 struck on March 1.

U.S. crude for July settled up 76 cents at $90.66 a barrel, after climbing to an early high of $91.52. On Wednesday, it settled at $89.90, the lowest close for front-month U.S. crude since October 21. U.S. crude is down about 19 percent from its 2012 high of $110.55, also hit on March 1.

Reflecting investor caution, volumes were light, with Brent trading down 30 percent from its 30-day average and U.S. crude dealings 45 percent lower from its 30-day average, according to Reuters data.

IRAN, GREECE SCENARIOS

Iran accused world powers of creating a difficult atmosphere that hindered negotiations on its atomic energy program, stalling diplomatic work to defuse fears of an Iranian attempt to develop nuclear bombs.

Iranian chief negotiator Saeed Jalili later insisted that Iran should have the right to nuclear fuel cycle and enrichment, adding that peaceful nuclear energy is the right of every nation.

After two days of inconclusive discussions, new talks will take place June 18-19 in Moscow to try to solve the long-standing dispute about Iran's nuclear program that caused tensions between Tehran and the West to lift oil prices to the year's high of more than $128 for Brent crude.

The market is now betting on Iran hardening its stance again, said Tamas Varga, analyst at brokers PVM Oil Associates in London. Given the Greek crisis, however, any rally should be fairly short-lived.

Meanwhile, European Union leaders, in an informal summit on Wednesday, pledged to support Greece remaining in the euro zone, but warned Greece had to stick to its side of its debt bailout bargain.

That situation has kept oil investors at a quandary on whether to buy back positions after recent sell-offs had left oil markets on both sides of the Atlantic in an oversold condition.

The rebounds on Thursday put the Relative Strength Index of both Brent and U.S. crude at around 26, from 23 on Wednesday, according to Reuters data, still below the 30 mark that signals oversold status.

The overriding factor in the market remains to be whether a Greek default will cause another credit crisis and contagion across Europe, said Gene McGillian, analyst at Tradition Energy in Stamford, Connecticut.

The euro edged up from near two-year lows against the dollar on Thursday as investors consolidated bearish bets on the common currency ahead of the long U.S. holiday weekend. But any bounce was likely to be fleeting as the market weighs the possibility of Greece exiting the euro zone.

Americans take to the road in force beginning this weekend to mark the U.S. Memorial Day holiday, with 30.7 million people expected to kick off the summer driving season, up from 30.3 million a year ago.

(Additional reporting by Robert Gibbons and Edward McAllister in New York and Christopher Johnson in London; Editing by David Gregorio and Bob Burgdorfer)