* Libya deal with rebels may make 500,000 bpd available for exports
* Iraq's Maliki hopes for government deal by next week
* U.S. crude inventories fall ahead of July 4 weekend -EIA
* Asian stocks hover at 3-yr high, U.S. jobs data enthrall
(Adds comments, updates prices)
SINGAPORE, July 3 (Reuters) - Brent futures dipped below $111 a barrel on Thursday as supply fears eased after Libya declared an end to an oil crisis that has cut exports from the OPEC member to a trickle, although declines will be capped by concerns over Iraq.
Libya's acting prime minister Abdullah al-Thinni said the government had reached a deal with a rebel leader controlling oil ports to hand over the last two terminals and end a blockade, making around 500,000 more barrels a day of crude available for export.
Brent crude extended the previous session's losses to fall to a three-week low, dropping 25 cents to $110.99 a barrel by 0621 GMT. U.S. oil declined 33 cents to $104.15, also sliding to a three-week trough.
"Even if Libyan production comes back, it will still be only 40-50 percent of the country's full pre-crisis exports. That's a small number," said Tetsu Emori, commodity fund manager at Japan's Astmax Investment. "People are still looking at Iraq."
Oil investors are on edge over how the crisis in Iraq can be brought under control, Emori said. With limited global spare production to fill up any major disruption in shipments from OPEC's second-largest producer, prices will head higher later this month, he said.
Iraqi Prime Minister Nuri al-Maliki said he hoped parliament could form a new government in its next session after the first collapsed in discord. Baghdad can ill afford a long delay as large swathes of the north and west fall under the control of an al Qaeda splinter group.
"Problems in Iraq come at the worst possible time for oil as the global economy is picking up momentum, oil demand growth embarks on a seasonal upturn and spare capacity continues to shrink," analysts at Barclays said in a note. "Oil markets are finely balanced and the risk of a price spike is greater than at any point since the start of the financial crisis."
Demand outlook is improving in the United States and China, the world's top two oil consumers.
U.S. crude stocks fell more than expected last week as refineries hiked output ahead of the holiday July 4 weekend, data from the Energy Information Administration showed.
Crude stocks dropped 3.2 million barrels compared with expectations for a decrease of 2.2 million barrels. Gasoline stocks fell 1.2 million barrels versus forecast of a 400,000-barrel gain, it said.
Employment growth in the country is expected to have continued at a solid clip in June further dispelling fears about the economy's health.
Earlier in the week, data from China showed factory activity hit multi-month highs in June, reinforcing signs that the world's second-largest economy is steadying.
Broader financial markets also gained on hopes of an improved economic outlook, with Asian stocks hovering at a three-year high and the dollar strengthening.
The improving demand outlook and lingering supply worries may push the U.S. benchmark towards $115 a barrel and Brent towards $120-$125 by the end of September, Astmax's Emori said.
"The market will be strong in July," Emori said. "We are seeing some liquidation, but prices will firm up. People are worried about supply."
(Reporting by Manash Goswami; Editing by Richard Pullin and Joseph Radford)