By Mariam Karouny

BAGHDAD, Oct 6 (Reuters) - Political paralysis and in-fighting is impeding the ability of Iraq's Shi'ite-led national unity government to tackle rampant violence and economic woes, an Iraqi Shi'ite leader said.

Vice President Adel Abdul Mahdi agreed with U.S. Secretary of State Condoleezza Rice's assertion on Thursday that factional wrangling had led to a dangerous stalemate inside the ruling coalition.

But Mahdi, one of two vice presidents and a senior Shi'ite Islamist, said U.S. involvement in Iraq was an important contributor to the problem.

"Decision-making centres have proliferated -- the Multinational Force, the Americans ... and also the very numerous political groups that have taken part in the democratic experience," Mahdi told Reuters.

"The most dangerous problem for Iraq today, for the economy, security and politics, is decision-making," he said in an interview on Thursday in his office in the fortified Green Zone government compound.

Since taking office in April, Prime Minister Nuri al-Maliki, also from the Shi'ite Islamist bloc which dominates parliament, has found virtually every decision challenged, whether by minority Sunni Arabs or Kurds or Shi'ite rivals, Mahdi said.

"The government's main mission is to overcome these obstacles. The parliament should help, the political blocs should also help in order to facilitate making security, political and economy decisions."

Other Shi'ite politicians, from the majority community oppressed under Saddam Hussein, have complained lately that U.S. pressure to form a power-sharing system among Iraq's three main groups has blocked them from exercising decisive majority rule.

RULES UNCLEAR

Referring to Saddam's overthrow, Mahdi said: "Since the fall of the tyrant, the Iraqi state has been stalled by a series of brakes that hinder the taking of any internal decision."

The U.S. military, whose commander General George Casey only last month began handing control of some Iraqi army units to Maliki, also needed to step back to a supporting role, he said.

"When the military presence is not regulated by an agreement, an Iraqi official cannot act in his own land and over his own forces in the way he should," he said.

"The rules of the relationship are not clear. We're always having discussions with them but so far nothing is finalised."

U.S. military officials say they are negotiating with the government on some form of agreement to regulate the presence of troops once their United Nations mandate expires in December.

Mahdi, a French-educated economist and former finance minister, is a leading figure in the Supreme Council for the Islamic Revolution in Iraq, backed by Iran to fight Saddam and led by Abdul Aziz al-Hakim.

Shi'ite leaders, many of them exiled under Saddam, strongly backed the U.S. invasion, while Saddam's fellow Sunnis tended to oppose it, often violently, and form the backbone of the insurgency.

With the spread of sectarian violence, however, many Sunni minority leaders have toned down calls for U.S. troops to leave, while some Shi'ites have become increasingly hostile to their presence and resent U.S. criticism of party militias many see as defending them against a return of Sunni-led oppression.

"Iraq now is a country with a sovereignty," Mahdi said. "The last word, even in the presence of the Multinational Force, is Iraq's."

"Friendly countries (should) have a supporting role only."

(Baghdad newsroom, Editing by Paul Hughes)

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