Officials at United Nations headquarters were surprised by Friday's announcement because U.N. envoy Lakhdar Brahimi was not present when the Iraqi Governing Council nominated Allawi.
"It's not how we expected it to happen," Fred Eckhard, chief U.N. spokesman said.
Despite the United Nations' surprise, officials said the international body "respects" the choice.
It was expected that Brahimi would announce the names in early June after consulting with Iraqi leaders.
"Mr. Brahimi respects the decision and is prepared to work with this person on the selection of the other posts in this interim government," Eckhard told reporters.
U.N. officials said that Brahimi's role had not been to name the government but facilitate the process.
"We were not invited to appoint the government," Ahmad Fawzi, Brahimi's spokesman said. "Now that it has been identified, we welcome the choice. We will be working with the prime minister-designate to appoint a cabinet, two vice presidents and a president."
Allawi, a wealthy businessman, will head the interim government that will take over power from the United States on June 30. The major task of the new government will be to organize elections.
The Bush administration supported Allawi's appointment.
"He will be the prime minister when the interim government is set up in the next two or three days," a senior administration official told reporters. "We thought he would be an excellent prime minister. ... I think that this is going to work."
He added, "We have endorsed this recommendation, the governing council has endorsed unanimously this recommendation, the Iraqis that he has talked to obviously (endorsed it)."
Allawi, a former Baathist, went into exile after he turned against Saddam and formed the Iraqi National Accord, a party made up of Iraqi military defectors that was backed by the CIA and British intelligence.
Allawi was the target of an assassination attempt in 1978 when Iraqi secret police came to London, entered his bedroom and attacked him with knives and axes. They left when his father-in-law arrived, according to the book, "Saddam Hussein -- An American Obsession," by Andrew Cockburn and Patrick Cockburn.
Allawi, a neurologist, is related to Ahmad Chalabi, who was thought of as a favorite to head the interim government before his recent fallout with Washington.
Not everyone endorsed the choice for the new prime minister, citing his time abroad as a cause for doubt.
"What is his political experience? I know nothing about him. He lived abroad as an exile. We need someone who lived here who can pull Iraq out of a crisis," a hotel manager told Reuters.
"Iraq is the same as it was in the time of Saddam Hussein except now I am afraid of militiamen so I can't say my name."
"I reject him," policeman Hassan Ali said. "Where was he when we suffered under Saddam? Besides I do not recognize the governing council."