John R. Bolton, now undersecretary of state for arms control and international security, was announced as Bush's choice for the post on Monday.
Known for his vocal criticism of the United Nations and sometimes caustic language, Bolton is likely to face a tough confirmation hearing in the US Senate, where even some Republicans have wondered aloud about the nomination.
Few governments commented publicly on the president's pick. But many in foreign-policy circles were wary of Bolton, seeing him as a staunch unilateralist indifferent to allies' views.
"This is really going to reopen all of the worst suspicions about the Bush administration's refusal to engage in effective multilateralism," Francois Heisbourg, director of the Paris-based Foundation for Strategic Research thinktank, said.
Others said the nomination showed Bush's seriousness about pushing for change at the United Nations.
Some in the Middle East saw his nomination as a sign that hardliners in favour of a more aggressive US policy abroad are gaining strength in Washington.
"This is an extremely bad message that Bush has submitted to the neo-conservatives," Imad Shuaibi, a Syrian political analyst in Damascus, said.
Iran vowed Tuesday to stand up to any heightened American pressure.
"The presence of hardliner Bolton in the UN prepares the ground for US intervention in the organisation," Iran's state-run radio said in a commentary.
Almost immediately after Bolton's nomination was announced, Democrats objected and even some Republicans wondered aloud about his fitness for the job.
While most said they will wait to hear his testimony at the Senate Foreign Relations Committee before deciding how to vote, many Democrats issued highly critical statements.
Bolton's nomination could be blocked by the committee on a tie vote if all of the Democrats, joined by one Republican, oppose him.
Despite the rift about his suitability, Bolton will probably be confirmed by the Republican-led US Senate, Majority Leader Bill Frist said on Tuesday.
"I think they will make it a challenge for us, but I think he will be confirmed. But they might make it very challenging," Frist, a Tennessee Republican, added.