Looking to step back from the brink, Iraq's fractious political blocs are working on short-term solutions to cool a crisis that threatened a slide back into sectarian strife, but fundamental differences may be left to smoulder.

Political leaders from Sunni Muslim, Shi'ite Muslim and Kurdish factions are looking to a national conference this month and the courts to defuse hostilities triggered when Shi'ite Prime Minister Nuri al-Maliki called for the arrest of Sunni Vice President Tareq al-Hashemi after the last U.S. troops left.

People are talking about dialogue. It does look like calm and wisdom are prevailing. I think we have stepped back, said one Western diplomat.

The outcome of the crisis has wider implications in a region where Syria's anti-government upheaval is taking on a sectarian tone and Shi'ite power Iran, Sunni Arab Gulf nations and Turkey to Iraq's north are all jostling to extend their influence.

At stake in Baghdad is the survival of an uneasy power-sharing government among Maliki's Shi'ite alliance, Sunni-backed Iraqiya and the Kurdish blocs that divides up ministries and posts but has struggled to work, hamstrung by deep mistrust.

In two apparent gestures over the past two days to calm the atmosphere, Maliki appealed for political stability and parliament speaker Osama al-Nujaifi called on Iraqis to build the present and the future with one heart and one hand.

The rival blocs appear to have agreed to attend the conference later this month proposed by Nujaifi, a Sunni, and President Jalal Talabani, a Kurd, and to let the courts resolve Maliki's allegations that Hashemi ran death squads.

But a senior Shi'ite politician who asked not to be named saw little hope that national dialogue would produce results.

It is not expected that this conference will offer anything new, but it offers an acceptable reason for Iraqiya leaders to end their boycott and save face, the lawmaker said.

For the moment, Iraqiya's boycott of parliament stands and suggestions for early elections -- not due until 2014 -- and other measures for long-term change are not gaining traction.

Whether Iraqiya's boycott survives may become apparent on Tuesday when parliament is due back from a recess and Maliki's cabinet convenes its regular weekly meeting.

Last week, two Iraqiya Sunni ministers, including Finance Minister Rafie al-Esawi, boycotted the cabinet and four were absent with excuses, but two others attended, highlighting the longstanding schism in the bloc.

A senior Shi'ite lawmaker said Sunday he was leaving the bloc over dissatisfaction with its leaders' decision-making and handling of the Hashemi crisis, joining 11 other Iraqiya lawmakers who have departed in the last three months.

Iraqiya is really divided, broken, said a senior Sunni leader in the bloc. All (its leaders) want is to go back to their jobs. Maliki humiliated Iraqiya (leaders) and now they are ready to sacrifice Hashemi.

If some Iraqiya ministers quit, others within the bloc may be ready to claim their jobs, strengthening Maliki's hand.

Should Iraqiya walk out or splinter, Maliki would likely turn to Kurdish partners and Iraqiya dissidents who have already split from their bloc, seeking a majority government.

The majority government is one of the options, not the only one, and not the current solution, said Kamal al-Sadi, a senior leader in Maliki's Dawa party.

Maliki could also face opposition within his own bloc, where some factions appeared to be using the crisis to push for a new prime minister or to negotiate for posts or other benefits.

Maliki's move against Hashemi and his demand that parliament dump Deputy Prime Minister Saleh al-Mutlaq, another Sunni leader, sparked Iraq's worst political crisis in a year.

The Shi'ite leader has presented Iraqiya with a challenge to sideline Hashemi, one of its senior leaders, or lose its sway in government. Iraqiya may ultimately have to decide whether it stays together or splinters, and cracks have already appeared.

Iraq's crisis could still go two ways: pulling back from the abyss once again or falling into deeper turmoil that shatters the frail cross-sectarian government and renews bloodshed after the mid-December withdrawal of the last U.S. forces.

ISLAMIST INSURGENTS

The rising tensions could unravel Iraq's U.S.-backed democratic experiment as the country's still-rebuilding security forces grapple with a weakened but still lethal al Qaeda-linked Sunni insurgency that carries out daily attacks.

Political infighting could open the door to foreign intervention and to Shi'ite and Sunni armed groups to ramp up attacks, reviving sectarian conflict.

Politics in Iraq, despite inflammatory rhetoric, is a slow boil with hours of back-room negotiations leading to deals. The power-sharing arrangement itself took more than half a year of horse-trading and cajoling as blocs bargained over posts.

U.S. Vice President Joe Biden, Maliki's Shi'ite partner anti-U.S. cleric Moqtada al-Sadr and Kurdish President Masoud Barzani have been odd bedfellows in trying to pull the government back together.

RISKY BACKLASH

But the major question now is Iraqiya's next move.

The party is in talks with other blocs and lobbying for a parliamentary vote of no confidence against Maliki. Any stand against Maliki will require backing from the Kurds and a Shi'ite bloc within Maliki's coalition.

Iraqiya will have to measure the potential loss of its government posts against any possible gain made by opting out of the government. It holds parliament speaker, a vice presidency, a deputy prime minister post and the finance ministry.

The risk for Maliki is if Iraqiya and the Kurdish blocs team up. But the Kurds may see more advantage in using the crisis as leverage to negotiate with Maliki over their own issues, such as control of oil resources and territories disputed between Baghdad and Iraqi Kurdistan, rather than backing Iraqiya.

Frankly, Kurds are not ready to sacrifice their strategic interests and alliances because of Hashemi, one senior Kurdish leader said. I don't think Iraqiya will succeed.

But Sunni discontent with Maliki is deep, and Iraqiya has already accused him of reneging on power-sharing agreements.

Nearly nine years after the invasion that overthrew Saddam Hussein, sectarian friction still runs close to the surface in Iraq, where sustained violence between Sunni and Shi'ite communities killed thousands of people in 2006-07.

Maliki's manoeuvres are fanning minority Sunni fears of political isolation. Since Saddam's fall, Iraq's Shi'ite majority has risen and Sunnis say they feel they have been pushed out of key decision-making.

Already, Sunni-dominated provinces like Anbar and Salahuddin are pressing for more autonomy from the central government, resisting what they see as Maliki's interest in pushing a Shi'ite agenda at the expense of Sunnis.

(Additional reporting and writing by Patrick Markey; Editing by Jim Loney and Mark Heinrich)