US Secretary of State Colin Powell has insisted that the decision on who will lead Iraq after the handover of power rests with the United Nations.
Allawi spent years in exile under Saddam Hussein
Earlier, the White House welcomed a decision by the Iraqi Governing Council to nominate Shia former exile Iyad Allawi as interim prime minister.
But Mr Powell said it was up to the UN special envoy to Iraq, Lakhdar Brahimi, to confirm the post.
The UN response has been cool, speaking only of "respect" for the decision.
When Iraqi sovereignty is returned on 30 June, the interim government will lead the country until national elections in 2005.
Mr Brahimi has been in Baghdad for a few weeks trying to put together a team including a prime minister, president, two vice-presidents and cabinet ministers.
IRAQ SELF-RULE TIMETABLE
30 June: Handover from Coalition Provisional Authority to interim government
End of Jan 2005: Elections to National Assembly
Autumn 2005: New constitution voted on in referendum
December 2005: Full elections for new government
January 2006: Directly elected government takes office
But the naming of Mr Allawi came from the Iraqi Governing Council in a surprise announcement on Friday.
"I'm pleased that Mr Allawi has that kind of support," Mr Powell told reporters in Washington.
"We have no position on any candidate at this moment because we are waiting to hear from Ambassador Brahimi and he needs time to complete his work."
Earlier, White House spokesman Scott McClellan said Mr Allawi was "a fine and capable leader who appears to have broad support among the Iraqi people".
The BBC's Jon Leyne, at the UN, says Mr Allawi was evidently not the first choice of the UN envoy.
Born 1945 to Shia merchant family
Trained in UK as a neurologist
Former Baathist, but fell out with Saddam Hussein
Co-founder of Iraqi National Accord
In New York, chief UN spokesman Fred Eckhard said: "It's not how we expected it to happen."
But he said Mr Brahimi "respects the decision and is prepared to work with this person on the selection of the other posts in this interim government".
A British government official in London said the Governing Council had named Mr Allawi prematurely, but the UK considered him a good choice.
Mr Allawi - a British-educated neurologist who left Iraq after turning against Saddam Hussein in the 1970s - was endorsed unanimously by the Governing Council.
Chief US administrator in Iraq Paul Bremer attended Friday's session of the Governing Council and congratulated Mr Allawi on his nomination, AP news agency reported.
The UN says Mr Brahimi was not even in the room when Mr Allawi was named by the IGC.
In 1978, while living in London, Mr Allawi survived an assassination allegedly ordered by Saddam Hussein.
He later became a founding member of the Iraqi National Accord, a group of exiles backed by US and British intelligence that included many former military officers opposed to the Baghdad regime.
Mr Brahimi had originally hoped to form a government of technocrats - people not associated with the main political parties which dominate the Governing Council.
But BBC Middle East analyst Roger Hardy says leading Shia members of the council resisted what they saw as Mr Brahimi's attempts to bypass them.
They are reported to have joined forces to oppose the appointment of respected scientist Hussein Shahristani as prime minister - and insisted that the top job should go to one of their own.