* U.S. equities markets rise on techs, banks
* U.S. jobless claims rise more than expected
* World oil demand to fall at fastest rate since 1981-IEA
* OPEC compliance with supply cuts slipping -IEA (Updates prices with U.S. settlement, Brent not yet settled)
NEW YORK, May 14 (Reuters) - U.S. oil prices rose on Thursday, tracking a rebound on Wall Street, though a gloomy demand forecast from the International Energy Agency (IEA) limited gains.
U.S. crude for June delivery <CLc1> rose 60 cents to settle at $58.62 a barrel while London Brent for June delivery <LCOc1>, which expired at the close of trade, fell 65 cents to $56.69 a barrel.
The gains in U.S. crude came alongside an uptick in equity markets led by technology and bank stocks. [
]Oil prices have been tracking equities markets in recent months as traders look to stocks for signs of an economic recovery that could lift ailing world fuel demand.
Gains were limited by a report from Paris-based IEA, adviser to 28 industrialized nations on energy policy, forecasting the steepest decline in world oil demand this year since 1981. [
]It said the rise in oil prices to a six-month high above $60 this week was due to sentiment rather than fundamentals.
The U.S. Energy Information Administration and OPEC also cut their forecasts for energy demand in recent days.
"The IEA report comes after the DOE and OPEC versions this month, which might lessen its impact, but it tells the same story as the others," said Tim Evans, energy analyst, Citi Futures Perspective, New York. "Demand is falling short of expectations."
The Organization of the Petroleum Exporting Countries (OPEC), which has announced 4.2 million bpd of production cuts since September in a bid to tighten the market, also pumped more oil last month than in March, the IEA said.
OPEC members' compliance with production quotas fell to 78 percent in April from 83 percent a month earlier.
The producer group next meets on May 28 and is unlikely to alter production limits if prices remain strong, Iraq's oil minister said Thursday. [
]Unrest in Nigeria, Africa's biggest oil producer, provided additional support for oil prices.
Nigeria's main militant group on Wednesday ordered oil workers in Africa's biggest oil producer to leave the delta within 24 hours following heavy clashes between MEND and security forces.
The Movement for the Emancipation of the Niger Delta (MEND) on Thursday gave oil companies an additional 48 hours to evacuate their staff, but threatened to attack helicopters and planes after the deadline. [
]A security source working in the oil industry said it was taking the threat seriously, but there were no plans to evacuate staff. (Reporting by Richard Valdmanis, Gene Ramos and Robert Gibbons in New York, Chua Baizhen in Singapore and David Sheppard in London; editing by Jim Marshall)