Wolfowitz, nominated on Wednesday by President George Bush, is widely seen as a key instigator in the US push to topple Iraqi leader Saddam Hussein.
International organisations are worried about the nominee's hawkish politics and questioned whether he is right for the job.
Bush, who has sought to mend ties with European allies that opposed the Iraq war, called French President Jacques Chirac to tell him the news.
Chirac, one of the staunchest critics of the war, "took note of this candidacy", his office said, adding that "France would examine it in the spirit of friendship between France and United States and with an eye on the capital mission of the World Bank to the service of development".
Japan, a US ally in the Iraq war, gave its support to Bush's choice.
"It's time for other candidates to come forward that have experience in development"
Jeffrey Sachs, director, Columbia University's Earth Institute
The Japanese Foreign Ministry said in a statement that Prime Minister Junichiro Koizumi expressed support for Wolfowitz in a phone conversation with Bush.
Chief Cabinet Secretary Hiroyuki Hosoda lavished praise on Wolfowitz. "He's a great person and he is well-versed in issues regarding development in Asia," Hosoda said. "Japan would like to support Mr Wolfowitz."
One of those most vocally opposed to the idea was UN Secretary-General Kofi Annan's top poverty adviser.
"It's time for other candidates to come forward that have experience in development," Professor Jeffrey Sachs, director of the Earth Institute at Columbia University and an Annan adviser, said in a speech to the UN Economic and Social Council.
"This is a position on which hundreds of millions of people depend for their lives," he said. "Let's have a proper leadership of professionalism."
The United Nations had no comment.
Development and anti-poverty groups joined the chorus of criticism.
"As well as lacking any relevant experience, he is a deeply divisive figure who is unlikely to move the bank toward a more pro-poor agenda"
policy officer for Action Aid
"As well as lacking any relevant experience, he is a deeply divisive figure who is unlikely to move the bank toward a more pro-poor agenda," said Patrick Watt, policy officer at British charity Action Aid.
Dave Timms, spokesman for London-based World Development Network, called it a "terrifying appointment" that highlighted a lack of democracy in major lending institutions.
A European traditionally heads the International Monetary fund, while an American takes the helm at the World Bank.
"You can't have a situation where rich countries lecture developing countries about democracy and then aren't prepared to exercise democracy in this kind of appointment."
A spokesman from the British government's Department for International Development said the nomination had been noted, adding: "The UK believes that broad support of the membership, including from developing country clients of the bank group, is key for the successful leadership of this institution in coming years."
Sweden's minister of International Development Cooperation, Carin Jaemtin, said she was "very sceptical" of the choice.
Wolfowitz's reputation as a
hardliner has hindered support
She told Swedish news agency TT that she had hoped for a candidate who would carry out the policies of outgoing bank president James Wolfensohn.
Wolfowitz, 61, was among the most forceful of those in the Bush administration in arguing that Saddam Hussein had weapons of mass destruction.
He had also predicted that Americans would be welcomed as liberators rather than occupiers once they toppled the Iraqi government.
Wolfowitz' reputation as a hardliner made it difficult to cheer his nomination to head the World Bank, said Nigerian newspaper columnist Pini Jason. He said it could a "bad omen" for the Third World.
"It is very likely that George Bush will want to link World Bank policies to his own vision of democratising the world: Democracy according to the White House," said Jason, who writes for The Vanguard newspaper.
Abd al-Bari Atwan, editor of the pan-Arab newspaper Al-Quds al-Arabi agreed.
"The appointment is another provocation from the US administration and the neo-conservatives to the Third World, especially the Arabs and Muslims."