* Crude inventories at highest ever in U.S. weigh on oil
* Libya's Zueitina port to resume oil loadings this week
* Investors eye data from euro zone, U.S. and China
* Coming up: U.S. nonfarm payrolls for April - 1230 GMT
SINGAPORE, May 2 (Reuters) - Brent crude held steady below $108 a barrel on Friday, on track for its steepest one-week decline in four months, as rising supply from the U.S. and Libya and a muted demand outlook in China dragged down oil prices.
Strong crude output in the United States pushed inventories to another record high last week, while the global market could see more oil coming out of Libya as the government resumed operations at the eastern Zueitina port.
Investors are looking ahead to economic data from the United States, the euro zone and China to gauge fuel demand outlook.
June Brent crude edged up 2 cents to $107.78 a barrel by 0606 GMT after settling on Thursday at its lowest close since April 11. U.S. crude was at $99.37 a barrel, down 5 cents, set to post a second weekly fall.
Some analysts also see an easing of the risk premium built into oil from the Ukraine crisis as investors turn their attention back to fundamentals.
"It's the lowering of rhetoric out of eastern Europe over the course of this week," said Michael McCarthy, chief strategist at CMC Markets in Sydney. "Supply is now starting to weigh on the complex and drag all of them down."
U.S. and European oil benchmarks tumbled mid-week after the U.S. Energy Information Administration released data showing a 1.7-million-barrel rise in U.S. crude stocks to just shy of 400 million barrels last week. Crude stocks are at their highest since the EIA started collecting data in 1982.
In Libya, state-run National Oil Corp (NOC) said on Thursday that the Zueitina port was expected to load its first tanker of crude since reopening after nearly ten months due to protests.
"Supply-wise, it's not so optimistic, because there is more concrete evidence of Libya coming back," Phillips Futures analyst Tan Chee Tat said.
Investors are awaiting manufacturing data from the euro zone and nonfarm payroll data from the United States later on Friday. HSBC will release on Monday its final survey on China's factory activity in April.
"These are likely to keep investors on the sidelines after a not-so-good performance in yesterday's macro release," Tan said, referring to China's official Purchasing Managers' Index on Thursday. The reading showed a slight pick-up in factory activity for April, although below economists' expectations.
U.S. employment likely rose at its fastest clip in five months in April, according to a Reuters survey of economists. Such a result would further confirm that world's largest economy is back on track after a dismal winter.
(Editing by Tom Hogue)