* Concerns over Iraq and Ukraine underpin prices
* U.S. crude stocks seen down 2.3 mln barrels, products build
(Updates prices, rewrites throughout)
NEW YORK, July 1 (Reuters) - Brent and U.S. oil prices declined on Tuesday on easing concerns of supply disruptions due to the conflicts in Iraq and Ukraine, though markets gained some support from upbeat manufacturing data in China, the world's second-biggest oil consumer.
"The market has been on a downtrend since peaking last week," said Dominick Chirichella of the Energy Management Institute in New York. "The latest data from China is interesting: it's not going to result in a big surge in oil demand anytime soon, but it's a baby step in the right direction."
China's factory activity hit multi-month highs in June, official and private surveys showed, reinforcing signs its economy is steadying as the government steps up policy support.
Brent crude fell 29 cents to $112.07 a barrel by 1:37 p.m. EDT (1737 GMT). U.S. oil fell 47 cents to $104.90 a barrel.
Oil markets have for weeks been rattled by supply concerns due to the Ukraine crisis, while a takeover of large areas of Iraq by Sunni militants has stoked fears of disruption in exports from OPEC's second-biggest producer.
Although oil exports have not been disrupted so far, the geopolitical uncertainty is likely to keep supporting prices in the short term, analysts said.
"Supply-related headlines and agitation (in Iraq and Ukraine) will keep the speculators on the long side of the market," said Thomas Saal, an analyst at INTL Hencorp Futures, LLC in Miami.
Iraq's new parliament convened on Tuesday under pressure to name a unity government to prevent the country from splitting apart after an onslaught by Sunni militants who have declared a "caliphate" to rule over the world's Muslims.
Meanwhile, in Ukraine, Kiev renewed military operations against pro-Russian separatists in the eastern part of the country, as Russian President Vladimir Putin vowed to protect the interests of ethnic Russians abroad.
With the market pointing "sideways," investors unloading net long positions ahead of the July 4 U.S. Independence Day holiday weekend may be driving the price down, said a futures broker in New York.
U.S. CRUDE INVENTORY FORECAST
The U.S. oil benchmark drew support from forecasts that crude inventories fell last week. A preliminary Reuters poll estimated a decline of 2.3 million barrels.
The survey took place ahead of weekly inventory reports from the American Petroleum Institute and the U.S. Energy Information Administration.
Oil prices also were supported by a slide in OPEC's output, which fell in June from a three-month high in May, a Reuters survey found, as fighting in Iraq closed the country's largest refinery and technical problems slowed exports from its southern region.
A Reuters monthly poll of 26 analysts forecast Brent crude oil would average $108 a barrel in 2014, the highest average forecast of a Reuters poll so far this year and well above the $105.90 average projected in last month's poll.
(Additional reporting by Ron Bousso in London and Manash Goswami in Singapore; Editing by Jason Neely, Keiron Henderson, Jessica Resnick-Ault, James Dalgleish and Paul Simao)