* Libyan rebels to reopen two oil terminals -spokesman
* Sunnis, Kurds shun Iraq parliament after no Maliki replacement named
* Despite Saudi pledge, another big oil outage would strain supply
* U.S. crude stocks fell by 876,000 barrels vs f'cast 2.2 mln bbl dip -API
By Manash Goswami
SINGAPORE, July 2 Brent futures slipped towards $112 a barrel on Wednesday as Libyan rebels agreed to reopen two oil terminals, but lingering worries over the threat of a sudden worsening in the Iraq crisis stemmed further losses.
The European benchmark dropped for a third day to trade near its lowest in nearly three weeks, but limited spare production capacity amid an improving demand outlook in China and the United States should help underpin prices.
Brent crude had eased 12 cents to $112.17 a barrel by 0311 GMT, after its lowest settlement since June 11. U.S. oil added 4 cents to $105.38, after also recording its lowest ending since June 11.
"We are looking at sideways movement in oil. The situation in the Middle East won't allow prices to go down," said Tony Nunan, oil risk manager at Mitsubishi Corp in Tokyo.
"The summer driving season is getting underway in the United States and China isn't falling off the cliff."
Libyan rebels blockading key eastern oil ports have agreed to reopen the remaining two terminals at Es Sider and Ras Lanuf. Since last summer, the port seizures have crippled Libya's oil industry.
If fulfilled, the deal would bring back around 500,000 barrels per day (bpd) of crude oil export capacity.
The overarching supply risks from Iraq and other key producers such as Nigeria amid a healthier demand picture look set to place the U.S. benchmark "firmly in the $100 camp", said Nunana.
Prior to Iraq conflict, Nunan assessed the fair value of the contract at around the $90-level. Brent is likely to similarly remain supported, he said.
Sunnis and Kurds walked out of the first session of Iraq's new parliament after Shi'ites failed to name a prime minister to replace Nuri al-Maliki, dimming any prospect of an early national unity government to save Iraq from collapse.
Prices have also been supported on worries of limited spare capacity to make up for any major loss in shipments. The world's unused spare oil production capacity would struggle to cover for another big outage, industry officials and analysts say, increasing the chance governments may tap strategic reserves should Iraq's southern exports be disrupted.
U.S. crude stocks fell by 876,000 barrels in the week to June 27 to 381.7 million, compared with expectations for a decrease of 2.2 million barrels, data from industry group the American Petroleum Institute showed on Tuesday.
Gasoline stocks dropped by 407,000 barrels versus forecasts of a 400,000-barrel gain. Distillate fuels stockpiles, which include diesel and heating oil, rose by 4.4 million barrels, against expectations of a 800,000-barrel gain, it said.
Investors are now awaiting official data from the Energy Information Administration (EIA) due later in the day to gauge the country's demand outlook. (Reporting by Manash Goswami; Editing by Joseph Radford)