* Supply falls by 70,000 bpd, led by Iraq
* Output edges higher in Saudi Arabia, Libya
* OPEC output back below supply target of 30 million bpd
By Alex Lawler
LONDON, June 30 (Reuters) - OPEC's oil output has fallen in June from May's three-month high, a Reuters survey found on Monday, as fighting in Iraq closed its largest oil refinery and technical problems slowed its southern exports.
The slight decline underlines how unrest and outages in the Middle East and Africa are taking their toll on OPEC supply, just as the International Energy Agency is highlighting a greater need for OPEC oil in the rest of the year. [D:nL5N0OU1KF]
Supply from the Organization of the Petroleum Exporting Countries has averaged 29.93 million barrels per day (bpd), down from 30.00 million bpd in May, according to the survey based on shipping data and information from sources at oil companies, OPEC and consultants.
The decline puts OPEC output back below the group's nominal target of 30 million bpd, which oil ministers decided at a June 11 meeting in Vienna to maintain for the rest of 2014.
OPEC pumps a third of the world's oil. In June, output has declined in Iraq and Iran, offsetting a modest increase in top exporter Saudi Arabia and smaller rises elsewhere in the group.
The largest decline came from Iraq, where production declined by 170,000 bpd according to the survey. Domestic crude use fell because of the closure of the Baiji refinery, which was attacked by militants.
Also, Iraq's southern exports fell. Shipments in the first three weeks of June were steady, but slowed to 2.43 million bpd over the whole month because of technical issues, from May's 2.58 million bpd.
At Iraq's southern terminals, one single point mooring is undergoing repairs to fix a broken mooring chain, while a berth at the Basra oil terminal is also undergoing maintenance, according to shipping sources.
The sale of three cargoes of crude by Kurdistan, in defiance of the central government, limited the decline in Iraqi exports, which in February had reached a record high of 2.8 million bpd.
Iranian crude exports also edged lower in June from May's elevated levels, the survey found. Higher exports since late 2013 following a softening of Western sanctions on Iran over its nuclear work have boosted OPEC supplies.
Nigerian supply declined slightly. Export schedules initially pointed to little change, but Royal Dutch Shell Plc declared force majeure at its EA field for repairs.
Of the countries which have boosted output, Saudi Arabia raised supply modestly, in part because of a higher need for crude in domestic power plants, industry sources said. Output also edged up in the United Arab Emirates.
Libyan supply rose by 30,000 bpd to a monthly average of 220,000 bpd, the survey found. Strikes and protests are still keeping output at a fraction of the country's potential. (Editing by William Hardy)