* Abadi under pressure to build consensus on reforms

* Support from top Shi'ite cleric vital

* Battle against Islamic State at stake

By Stephen Kalin and Ahmed Rasheed

BAGHDAD, Nov 10 (Reuters) - Facing resistance from within his own party, Iraqi Prime Minister Haider al-Abadi is struggling to sustain support for a political shake-up he says is critical to efforts to counter Islamic State militants.

In an attempt to regain momentum after parliament last week blocked his government from passing important reforms without its approval, Abadi reached out over the weekend to Iraq's powerful Shi'ite Muslim establishment, which has previously backed his anti-corruption push.

But he returned from meetings with senior clerics in the sacred Shi'ite city of Najaf without securing fresh support, raising the prospect of further isolation as he seeks to head off the threat of a no confidence vote by disgruntled lawmakers.

In Najaf, Abadi notably did not meet with Iraq's top Shi'ite religious figure, Grand Ayatollah Ali al-Sistani. Sistani and the other clerics have backed Abadi but seem to have become impatient with the slow pace of reform.

"It's as though he is walking through a minefield," said Baghdad-based political analyst Ahmed Younis, citing pressures from parliament, the public, and Shi'ite religious authorities. "He is now obligated to work in a way that pleases all sides."

History suggests he should proceed with caution. Abadi's predecessor, Nuri al-Maliki, was also perceived as a leader who did not consult before taking decisions.

He was pushed out last summer after alienating his own party and fellow Shi'ites, as well as American allies and regional power Iran, which has wide sway in Iraq.

Iraq's power brokers, including the Shi'ite religious establishment, supported Abadi as the new prime minister after concluding he was a consensus builder who had a chance of healing political and sectarian divisions.

The biggest challenge for Abadi is reforming Iraq's notoriously corrupt military -- which has largely collapsed in the face of Islamic State advances -- and streamlining a government seen as inept.

Emboldened by popular protests in Baghdad and other cities and a call for action by Sistani, Abadi unilaterally launched a reform campaign in August.

He moved to dismantle Iraq's patronage system and root out incompetence and corruption undermining the major OPEC oil exporter's battle against Islamic State militants who have seized nearly a third of the country's territory.

Those measures soon got bogged down by legal challenges and opposition from entrenched interests. Frustrated by inaction, protesters demanding an end to corruption and better water and electricity services began to call Abadi weak and ineffective.

Sistani has also expressed displeasure with delays in enacting reforms, calling on Abadi to take bolder action in the face of resistance.

Though the reclusive octogenarian rarely hosts politicians, a meeting in Najaf would have shored up Abadi against the increasingly popular Iranian-backed Shi'ite militias and politicians like Maliki, who have sought to maintain privileges targeted by the reforms.

Their aims are causing a split among Iraq's Shi'ite leaders, further fragmenting a country struggling to contain Islamic State, the biggest security threat since a U.S.-led invasion toppled autocrat Saddam Hussein in 2003.

"It was a setback," Sami Askari, a lawmaker from the ruling State of Law coalition, said of the Najaf trip. "I'm sure Abadi came back unhappy, because if he had been able to see Sistani it would balance all the movement of the parliament."

A spokesman for Abadi said no such meeting was ever requested, but a source close to the prime minister described the fact that he did not meet Sistani as "negative".

FADED MANDATE

With his once indisputable mandate from the protesters and Sistani faded, Abadi may no longer be in a position to challenge those who oppose his reform drive.

The toughest demands could come from within his own State of Law coalition, which led last week's vote asserting parliament's authority after it demanded wider consultation from Abadi.

While the lawmakers' resistance is focused on the reforms, it stems from larger disagreements between two camps inside State of Law headed, respectively, by Abadi and Maliki.

Maliki's supporters, who are allied with Iran, regard Abadi as too close to the United States, which arms and trains Iraqi forces and is leading an air campaign against Islamic State. Maliki himself is popular with the Iranian-backed militias, seen as a bulwark against the Sunni insurgents.

"Abadi sometimes feels that this is a threat to his authority and he tried hard to weaken Maliki," said Askari.

Abadi has failed to enforce one of his main reforms which would have removed Maliki and the two other vice presidents from their positions. Instead Maliki is holding on, setting himself on a collision course with Abadi.

"The more (Abadi) pressures Maliki, the more he will lose the support of the State of Law," said Askari.

State of Law members dismiss speculation that Abadi has begun courting outside parties to form a new coalition to support his reforms. They warn such a move would require major concessions and expose him to attacks from his own base.

But lawmakers say Abadi may still need broader support to ensure his proposals pass through parliament smoothly and to prevent the possibility of a vote of no confidence, which lawmakers have not ruled out.

Backing from Shi'ite clerics Abadi met over the weekend, who are largely opposed to Maliki, could prove critical in any future confrontation, but this seems unlikely under present circumstances.

Meanwhile, backing from other Shi'ite groups, such as the Sadrists or the Islamic Supreme Council of Iraq, would enable Abadi to block a coup from within his own electoral alliance, said the source close to the prime minister.

"It's just to make sure that he's got members in parliament that would block any move down the road to withdraw confidence," the source said.

"A smattering of support from the Kurds or from a Sunni party means you're making sure they won't reach the 60 percent they need. It's a preemptive motion."

(Editing by Michael Georgy and Giles Elgood) ((michael.georgy@thomsonreuters.com;)(M +2010 271 00098)(O +20 225783290; Reuters Messaging: michael.georgy.thomsonreuters.com@reuters.net))