Dawa, the oldest Shia party in Iraq, discourages its supporters from joining Mr Sadr's rallies.
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Mr Maliki's Dawa party and the INA could still make up, but the gulf appears deep.
That would allow him, if elected, to cement Dawa's position ahead of the more hardline sectarian parties.
The alliance includes al-Maliki's Dawa Party and the Islamic Supreme Council of Iraq.
Iraq's oldest and possibly most popular Shia party, Dawa, slowly re-merging from the underground, also has reservations about Mr Sistani.
"Maliki and his Dawa party are big winners everywhere and particularly so in the big cities of Basra and Baghdad, " Visser said.
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He was opposed to Saddam Hussein and was a member of an Islamic party called the Dawa party, which was outlawed by Saddam in 1980.
In the classroom next door, 21-year-old Dechen Dema gulps hard as her tutor, Dawa Tshering, presents the artwork she must attempt to replicate.
On Friday, the Shiite-led political bloc, the United Iraqi Alliance, put forward al-Maliki of the Dawa Party as its candidate to replace al-Jaafari.
Almost certainly, Mr Talabani will be Iraq's president and Dr Ibrahim al-Jaafari, who heads the Dawa party within the Shia alliance, prime minister.
Reports say Pakistani police have also ordered the sealing of some offices used by Jamaat-ud-Dawa, the Islamic charity seen as a front for Lashkar-e-Taiba.
And al-Maliki, who is a member of the Dawa Party, which is a very religious organization, it calls for the Shia religious leadership to direct the government.
Mr Allawi did even better as an individual, polling at 35% against 11% for his closest competitor, Ibrahim al-Jaafari of the Dawa Party, probably the Alliance's strongest component.
Mr Maliki, though lacking much of a base in his own small Dawa party, is increasingly putting his own men in top spots in the security forces and key ministries.
Jack Reed said Iran has close ties to all of Iraq's Shiite factions, including al-Maliki's Dawa party and the country's largest Shiite religious party, the Islamic Supreme Council of Iraq.
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The United Iraqi Alliance on Sunday night discussed the draft, which was presented by Iraqi Prime Minister Nuri al-Maliki, whose Dawa Party is also a member of the ruling bloc.
In addition, much of Prime Minister Nuri al-Maliki's Dawa Party leadership took refuge in Iran before Hussein's overthrow by a U.S.-led army in 2003, though al-Maliki himself was in exile in Syria.
Shiite Vice President Adel Abdul Mehdi of the Islamic Supreme Council of Iraq, addressing the meeting, said he wished the Dawa party had been present at Monday's announcement, but negotiations will continue.
Their finance ministers got together in Kuala Lumpur and at the keynote address from the finance minister from the host nation of Malaysia, he encouraged the shariah finance industry to keep conducting its dawa operations.
The prime minister's State of Law Coalition, which mainly includes members of his Dawa party, won control of most of the country's provincial councils in January's elections, turning back mainly Islamic Supreme Council of Iraq opposition.
After joining Tablighi Jamaat groups at a local mosque or Islamic center and doing a few local dawa (proselytism) missions, Tablighi officials invite star recruits to the Tablighi center in Raiwind, Pakistan, for four months of additional missionary training.
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Al-Maliki's Dawa Party has been trying to avert a governmental collapse by entering into an alliance with another Shiite party and the two top Kurdish parties, but it has not been able to attract a top Sunni party to join its effort.
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These forces, who receive no money from Iran and Saudi Arabia to buy votes, and have no private militias to intimidate voters, couldn't compete against the likes of the Dawa party in Iraq, the Muslim Brotherhood in Egypt or Fatah and Hamas in the Palestinian Authority.
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