BAGHDAD, Aug 29 (Reuters) - A battle between militiamen and Iraqi troops that left dozens dead highlighted deep fractures among Shi'ite parties united in the Baghdad coalition government but warring for influence over the oil-rich Shi'ite south.

Relatively unscathed by the three-year-old insurgency by once dominant minority Sunni Arabs and the death squad response that has turned the capital into a killing field this year, the cities south of Baghdad are seeing bitter factional struggles that can turn very bloody -- as in Diwaniya on Monday.

At the heart of the fighting in Diwaniya, a provincial capital in the fertile Middle Euphrates plain, appear to have been fighters from the Mehdi Army militia, even though senior political officials close to its clerical leader Moqtada al-Sadr denied involvement in a battle that killed at least 20 soldiers.

Sadr's movement, popular among poor and long-oppressed Shi'ites for charity work modelled on Lebanon's Iranian-backed Hizbollah, is one of a handful of major Shi'ite parties grouped in the United Alliance, which dominates parliament and Prime Minister Nuri al-Maliki's U.S.-backed national unity government.

Among the most vocal is the Supreme Council for the Islamic Revolution in Iraq (SCIRI), led by Abdul Aziz al-Hakim. Founded in Iran to oppose Saddam Hussein, it also has an armed wing, the Badr movement. Maliki's Dawa party also enjoys wide support.

The smaller Fadhila party has risen to prominence by holding powerful posts in Basra, Iraq's second city and the hub of the great southern oilfield, the key to much of the national wealth.

Rivalries among the factions contributed to a six-month delay in forming a government and pose a challenge to adhering to consistent government policies and to the smooth running of local administration in much of southern Iraq.

Sadr, who led two uprisings against U.S. troops in 2004, is outspokenly critical of the occupation while Hakim has been more cooperative with Washington. Uneven and shifting relations with Tehran also mark the relationships among Shi'ite factions.

Maliki is already planning a reshuffle of his government, senior officials say, because of frustration with nominal allies thwarting his efforts to reconcile Iraq's communities. He has made little obvious progress on a pledge to disarm militias.

VARYING ALLIANCES

Alliances and rivalries vary across the south, depending on local conditions.

On Monday, it took talks in the nearby Shi'ite religious centre of Najaf between Sadr and the province's SCIRI governor to calm things down in Diwaniya. It was unclear what, if any, role was played by officials in the central government.

In Basra, SCIRI and Sadr supporters have set aside long- standing rivalries to counter Fadhila's strength, centred on the figure of the provincial governor.

In Kut, on the Tigris river southeast of Baghdad, there is tension between followers of Shi'ite cleric Mahmoud al-Hasani, a critic of the government, and the police chief, from SCIRI.

Hasani's followers marched in their hundreds through the streets of Kut to the alarm of local authorities last month.

In Samawa, the first province to be handed over by foreign troops to Iraqi control last month, tension between Sadr followers and the SCIRI governor has frequently boiled over into clashes, with Sadr's supporters in the vanguard of complaints about poverty and lack of local amenities.

In a calming gesture, Sadr changed his movement's main preacher in Samawa, appointing a more moderate spokesman.

Throughout the south, well-funded Shi'ite parties increase their grassroots support by providing essential services where the government has failed, primarily in health and education.

SCIRI, for example, even sponsors some local sports teams.

Parties also try to capitalise on the diverse religious loyalties typical of Shi'ites, where the faithful follow the spiritual lead of one or other of a number of senior clerics.

One tendency is for rival parties to associate their propaganda with the image of Grand Ayatollah Ali al-Sistani, the most influential of these religious authorities.

Sistani, an elderly recluse, helped unite the factions into the United Alliance. But some see his influence waning as militia violence rises despite his calls for restraint -- adding to doubts about the Alliance's future.

(Additional reporting by Alastair Macdonald and Reuters reporters in Diwaniya, Basra, Kut, Samawa and Basra)