BAGHDAD, Iraq — Hours after ending two days of meetings with Donald Rumsfeld and Condoleezza Rice, the Iraqi prime minister-designate, Nouri al-Maliki, traveled to the Shiite holy city of Najaf to convene with two of the real powers he must now contend with, the Shiite leaders Grand Ayatollah Ali al-Sistani and Muqtada al-Sadr.

Violence cast a shadow on the meetings, with the drive-by assassination in Baghdad of the sister of vice president Tariq al-Hashemi and the deaths of one Romanian and three Italian troops near Nasiriyah, which spurred calls from some Italian political leaders to speed the withdrawal of the country's 2,600 remaining troops in Iraq.

In his meeting with al-Sistani, al-Maliki won a statement from the revered religious leader calling for an end to militias and urging that the Iraqi security forces be freed from the grip of sectarian and political dominance. "Weapons should be carried only by government forces" loyal to the government and not to leaders of political or other groups, he said.

It was a firm message of support for al-Maliki, who said Thursday he believed he could complete selection of his Cabinet within a week. With prodding from the American ambassador, Zalmay Khalilzad, al-Maliki has made a priority of reducing the influence of the militias that have helped push Iraq to the brink of civil war. Sunni Arab leaders say that hundreds of young Sunni men who have been found murdered with drill holes in their limbs or head or other signs of torture are the victims of Shiite death squads, often wearing official police or commando uniforms.

But making a dent in the militias' influence will be very difficult to accomplish, as some elements of the Iraqi army and security forces are already dominated by members who proclaim loyalty to one militia or another. Other Shiite leaders have complained that American officials have gone too far in reining in the ability of Shiite-controlled security forces to combat the Sunni-dominated insurgency.

Indeed, in a demonstration of the balancing act al-Maliki must perform both as prime minister and as head of a fractious Shiite coalition, he met next with the anti-American al-Sadr, who oversees a thousands-strong militia of young Shiite men who control northeastern Baghdad and have fought fierce battles with the American military. Al-Maliki was careful not to offend al-Sadr, perhaps the most influential single force in the Shiite coalition, suggesting that militias deserve to remain an influence, even if only from within the military.

"Merging the militias into the military," al-Maliki said, "is not to disrespect them but to reward them for their role in the struggle against dictatorship," a reference to fighting by Kurdish and Shiite forces against Saddam Hussein. "And it is a solution to the problem of having weapons outside the government."

Al-Maliki's political pilgrimage to Najaf came as Baghdad residents were reminded that even the most powerful Iraqi leaders cannot protect family members from the savage violence here. Al-Hashemi's sister was gunned down in a morning rush-hour ambush near her home — just two weeks after the murder of al-Hashemi's brother — in another indication of how insurgents are intent on terrorizing leaders of the new government. While government leaders are heavily guarded, their loved ones are often easier targets.

Maysoon al-Hashemi, 61, who was director of women's affairs in her brother's Iraqi Islamic Party, was buried a few hours later amid elegies from co-workers who recalled how she bravely took the news that her brother Mahmoud had been assassinated on April 13. Insurgents also killed the brother of a Sunni leader, Saleh al-Mutlak, this month, and last fall they killed the brother of a Shiite leader, Adel Abdul Mahdi, Iraq's other newly selected vice president.

Inside the Green Zone Thursday, an American military spokesman offered an optimistic view, saying Iraq was "moving away" from civil war.

"All indications now are the acts of violence — ethno-sectarian violence is decreasing," Maj. Gen. Rick Lynch said at a news briefing. He cited a 60 percent decrease in casualties in the week starting April 16 through April 22 compared to the week before. Yet he also acknowledged that casualties have soared by 90 percent in the past 10 weeks, since before the bombing of the Askariya Shrine in Samarra in late February set off a wave of sectarian violence.

Other newly released American government findings cast Iraq's situation in less positive terms. The Government Accountability Office, the investigative arm of Congress, reported that attacks against coalition forces, Iraqis and infrastructure increased 23 percent from 2004 to 2005.

"The insurgency intensified through October 2005 and has remained strong and resilient since then," the GAO said in a 31-page report. "Many Iraqis in Baghdad and the central and northern Sunni areas have lost confidence in the Iraqi army and police to improve the security situation. In some Sunni areas, support for the insurgents has increased, and Iraqi Shiites have expressed greater confidence in their militias.

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The GAO also found that in contrast to past assertions that only four Iraqi provinces are suffering serious problems, in reality six are in "serious" shape and one is "critical." The finding, based on a joint study by the military and American Embassy in Baghdad, was first reported by the New York Times on April 9.

Before departing, Rice and Rumsfeld voiced support again for al-Maliki as a leader who can re-establish confidence in the government, while Iraq's national security adviser, Dr. Muwaffak al-Rubaie, suggested there could be a large reduction in American troops by 2007.

Al-Maliki also pledged to name nonsectarian appointees to head the ministries of interior and defense.

But in Najaf, al-Sadr had only harsh words for the Americans, calling their visit an "obvious interference in Iraq's affairs."

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