* Spike in U.S. service sector growth offers relief from China's slowdown
* Pro-Russian rebels shoot down a Ukrainian helicopter; violence moved west
* U.S. crude stocks forecast to rise 1.5 million barrels last week
* Coming up: U.S. API inventory report due 2030 GMT
By Jacob Gronholt-Pedersen
SINGAPORE, May 6 (Reuters) - Brent crude held steady below $108 per barrel on Tuesday as clashes across Ukraine added to geopolitical risk supporting a market that might otherwise sag due to expectations weekly data will show higher inventories in the United States.
Data released overnight showing a spike in U.S. service sector growth could offset some of the pessimism generated by disappointing Chinese manufacturing data.
Brent crude for June delivery was 3 cents lower at $107.69 per barrel by 0336 GMT, after settling 87 cents down. U.S. oil was also 3 cents lower at $99.45, following a fall of 28 cents on Monday.
"The services data adds more evidence that the U.S. economy is indeed recovering, helping lift the prospect for crude oil demand in the United States," said Chee Tat Tan, an investment analyst at Phillip Futures in Singapore.
In Ukraine, pro-Russian rebels shot down a Ukrainian helicopter in fierce fighting near the eastern town of Slaviansk, while Kiev drafted police special forces to the port city of Odessa to stop the rebellion spreading westward.
In one of the first signs that the conflict has impacted Russian energy shipments, Russia's state pipeline operator stopped diesel shipments to Ukraine and Hungary last month due to uncertainties over the pipe's ownership.
RISING U.S. STOCKS
Oil prices remain subdued by plentiful supplies, with U.S. commercial crude oil inventories forecast to have hit a new record high for the third week in a row due to higher imports.
The American Petroleum Institute (API), an industry group, is due to issue its weekly inventory report at 2030 GMT, while the U.S. Department of Energy's Energy Information Administration (EIA) will issue it report on Wednesday.
A preliminary Reuters poll of five analysts, taken ahead of reports, showed expectations centering round a rise of 1.5 million barrels in crude oil stocks for the week ended May 2.
EIA data wiped 2 percent off U.S. oil futures last week by showing U.S. crude stocks hit a record high on the week ending on April 25, led by another steep increase on the Gulf Coast.
"The concern is that the market cannot keep up with the pace of production," said Chee Tat Tan.
Higher Libyan exports have also put pressure on oil prices in recent weeks. The country's oil production currently stands at 250,000 barrels a day, but the vital southern El Sharara oilfield remains closed, a spokesman for state-run National Oil Corp (NOC) said on Monday.
A new protest has shut down the Zultun and Raquba oilfields in central eastern Libya, halting their combined output of 39,000 bpd, the spokesman said. (Reporting By Jacob Gronholt-Pedersen; Editing by Simon Cameron-Moore)