* Asian stock markets follow Wall Street higher
* Dollar steady, holds near four-month lows
* World oil demand to fall at fastest rate since 1981 - IEA
By Chua Baizhen
SINGAPORE, May 15 (Reuters) - Oil prices paused below $59 on Friday as investors weighed stronger equities, a steady dollar and a gloomy demand forecast by the International Energy Agency.
Crude prices were just a notch higher from last week's close, after moving in lockstep with the stock market and rising against a bearish report by the IEA a day earlier.
U.S. crude for June delivery <CLc1> inched up 9 cents to $58.71 a barrel at 0246 GMT, while London Brent for July delivery <LCOc1> rose 12 cents to $58.71 in its first session of trade as the new front-month contract.
"Equities and currency are most important. The $60 price level is also very important," Tetsu Emori, a fund manager at Tokyo-based Astmax Co Ltd, said.
U.S. oil prices breached $60 a barrel during intraday trading on Tuesday but settled below $59 after the U.S. Department of Energy slashed its 2009 oil demand forecast.
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.
Tokyo's Nikkei average <
> was up 1.66 percent by the midday trading break after Wall Street closed firmer on Thursday, while the dollar was steady against a basket of major currencies <.DXY>. [ ][ ]Paris-based IEA, an adviser to 28 industrialized nations on energy policy, forecast a day earlier that world oil demand this year would fall the most since 1981. [
]IEA 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.
"I don't expect oil demand to recover any time soon," Astmax's Emori said.
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.
Traders will take cues from more economic indicators out of the United States due later in the day, as well as renewed unrest in Nigeria, Africa's biggest oil producer.
Nigerian militants have hijacked two cargo ships in the Niger Delta and given oil companies until Saturday to evacuate staff, warning they would attack helicopters and planes after the deadline, after heavy clashes with the military. [
]Economic data expected later include U.S. April consumer price index, the Reuters/University of Michigan survey of May consumer sentiment, the U.S. ECRI weekly index of economic activity, as well as euro zone flash first-quarter GDP. (Editing by Ben Tan)