The selection of Iyad Allawi — a Shiite Muslim council member who headed an exile group made up of former Saddam military officers — was an assertion of influence by the U.S.-picked body.
The White House on Friday gave a glowing endorsement of Allawi after initially expressing hesitancy about the choice of the once-exiled Shiite Muslim.
"He is certainly a fine and capable leader who appears to have broad support among the Iraqi people," spokesman Scott McClellan said.
The White House had said earlier in the day that Allawi was just one of many candidates and the council was one of many groups offering names.
U.N. envoy Lakhdar Brahimi, who has been leading discussions on forming the government, also all but endorsed Allawi. Brahimi "is perfectly comfortable with how the process is proceeding so far," a statement by his office said.
The United Nations acknowledged the timing of the council's announcement was a surprise, but said Brahimi would work with Allawi on the makeup of the government, due to be announced in the coming days.
CBS News Correspondent David Hawkins reports Allawi is a neurologist and businessman, a former Baath Party member who went into exile in 1971. His opposition group, the Iraqi National Accord, plotted coups against Saddam. In 1978 Allawi escaped assassination by the former regime's hired killers.
In other developments:
Allawi had been "high on (Brahimi's) list" of possible premiers," spokesman Fred Eckhard said at U.N. headquarters in New York. The announcement "is not how we expected it to happen ... but the Iraqis seem to agree on this candidate."
Allawi, a moderate Shiite Muslim, has a long history of dealings with the United States, including the CIA. A surgeon and businessman, he also launched an expensive lobbying campaign last year to build relationships with U.S. policy-makers and has been developing relationships in his native Iraq.
Allawi is a former Baath Party member whose wealthy family was close to the royal family that ruled before Saddam Hussein took power After falling out of favor with Saddam, Allawi sought exile in London. He was badly wounded thre in an assassination attempt while living in the UK in 1978, believed to have been ordered by Saddam.
Still to be chosen for the new government are a president, two vice presidents and 26 Cabinet members. The president, a largely symbolic post, is to be a Sunni, and the vice presidents are expected to be a Kurd and a Shiite.
Allawi has maintained a low profile here and is believed to have only a limited power base in Iraq.
But council members wanted a prime minister with a strong background in security to deal with the persistent violence that will be the most compelling challenge for the new government.
Allawi's Iraqi National Accord party included many army officers who defected during Saddam's rule, and a relative serves as Iraq's minister of defense. He is also a member of the majority Shiite community, whose leaders had insisted that one of their own take the most powerful government post.
The choice was a rejection of Brahimi's initial preference for a weak government of nonpolitical figures to take power June 30 and prepare for national elections by Jan. 31.
Absent any opposition, however, it appeared the United Nations had little choice but to accept the Governing Council decision, given international demands for the Iraqis to have a greater say in their own affairs.
A U.N. official said Brahimi had advance word that the council would pick Allawi, and that Brahimi, while respecting Allawi's abilities, was concerned about his close identification with the Americans and the CIA.
Governing Council member Raja Habib al-Khuzaai told Associated Press Television News that the decision to select Allawi occurred at a special meeting which began at 3 p.m. Friday. Twenty of the council's 22 members were present or represented at the session; all voted for Allawi.
The U.S. governor of Iraq, L. Paul Bremer, was invited to join the session at 4 p.m., and Brahimi was invited an hour later — ostensibly to discuss other issues. Each was informed of the council decision when he arrived, al-Khuzaai said.
Soon after, Brahimi signaled his acceptance. His spokesman, Ahmad Fawzi, told The Associated Press , "Very, very soon, we will be discussing with the prime minister-designate the formation of the whole Cabinet."
In New York, Eckhard said Allawi must have support from a broad Iraqi political spectrum, saying: "Let's see what the Iraqi street has to say about this name."
The statement by Brahimi's office appeared to accept the prime minister's post as filled, saying "the interim government, its president and vice presidents included ... (is) still to be formed."
Bremer spokesman Dan Senor told reporters that Bremer attended the session "after the Governing Council had voted on their endorsement for prime minister and congratulated the Governing Council on a very distinguished choice."
The council decision came two days after the purported front-runner, nuclear scientist Hussain al-Shahristani, a Shiite, announced he was not interested in the post — apparently because established Shiite political factions objected.
Allawi and other Shiite former exiles — Ahmad Chalabi, Ibrahim al-Jaafari and Abdel-Aziz al-Hakim — also argued that Iraq needed a strong prime minister.
His "nomination has a great deal to do with security since it's ... our main problem," council member Mahmoud Othman said.
Those concerns have become more acute as the countdown to sovereignty continues. Despite an agreement to end fighting around Najaf, a Shiite rebellion led by radical cleric Muqtada al-Sadr continues, as does a Sunni insurgency in central Iraq.
Baghdad and other cities have been rocked by car bombings, including an attack May 17 that killed the head of the Governing Council, Izzadine Saleem.
On Thursday, gunmen ambushed the convoy of council member Salama al-Khafaji, killing a bodyguard and her son.
Allawi had been involved in the opposition since the 1970s, organizing various groups and coordinating policies with his backers in Washington — particularly the CIA and State Department.
He has long been seen as a rival of Chalabi, his fellow council member once groomed by the Pentagon as a possible successor to Saddam. The two, however, worked together in coordinating between anti-Saddam exile groups.
Chalabi did not attend Friday's council meeting, but his representative voted in favor of Allawi, according to members.
While living in London in 1978, Allawi survived an assassination attempt believed to have been ordered by Saddam. His Iraqi National Accord advocated a coup against Saddam, but an attempt in 1996 failed.