* Fresh conflict in Syria supports prices
* Weak demand outlook, well supplied market weigh
* Coming Up: API weekly crude stock report; 2030 GMT (Updates prices, adds quote)
By Ramya Venugopal
CHENNAI, India, May 21 (Reuters) - Brent crude futures steadied near a two-week high on Tuesday, holding around $105 per barrel as rising Middle East tensions offset concerns about moderating demand growth to keep prices in a tight range.
Reports that Lebanese Hezbollah guerillas were involved in fierce fighting for Syria's embattled president prompted alarm the civil war may spread to neighbouring oil producers, while a weakening dollar added to support.
Bearing down on prices are concerns that data this week may show sluggish growth in major consuming economies, adding to high inventory levels and expectations of increased supply.
"The conflict in Syria looks like it's getting serious and the dollar is heading lower, while continuing high inventories are putting downward pressure on prices," said Victor Shum, managing director of IHS Consulting in Singapore.
"(But) given the physical fundamentals, I expect prices to moderate from current levels, unless the situation in Syria flares up further," he said.
Front-month Brent futures added 6 cents to $104.86 per barrel by 0415 GMT, after touching $105.31 in the previous session, the highest since May 7.
U.S. crude fell 7 cents to $96.54 but could gain support from inventory data due on Tuesday, which may show a drop in crude stockpiles, according to a Reuters poll.
"Seasonal Asian oil demand (is) not expected to pick up until June, (so) we expect prices to remain in the $100-105/bbl range," ANZ analysts wrote in a report.
Initial estimates of Purchasing Managers' Indexes (PMIs) are due this week for China, the euro zone and the United States, but are unlikely to dispel fears of a sluggish global outlook, Reuters polls show.
Hghlighting these concerns, UBS trimmed its forecast for economic growth in China, the world's biggest energy consumer, citing weak credit expansion and credit growth.
"While some of the weakness may be transitory, increasingly evidence suggests that growth will be weaker than we previously envisaged," Tao Wang, UBS China economist, wrote in a report.
U.S. inventory data due later on Tuesday may support oil prices if the numbers are in line with expectations for a 400,000 barrel fall in U.S. commercial crude oil stockpiles on higher refinery activity and lower imports, according to a preliminary Reuters poll.
The dollar also offered support, falling against a basket of currencies as traders pared back expectations Federal Reserve Chairman Ben Bernanke would hint at tapering U.S. bond purchases when he testifies to Congress on Wednesday.
A weaker dollar makes U.S. dollar denominated commodities cheaper for holders of other currencies.
(Reporting by Ramya Venugopal; Editing by Clarence Fernandez and Richard Pullin)