Addressing a New York conference on global leadership on Tuesday, UN Deputy Secretary General Mark Malloch Brown slammed what he called the prevailing US "practice of seeking to use the UN almost by stealth as a diplomatic tool while failing to stand up for it against its domestic critics."
Mr Malloch Brown said that while Washington is constructively engaged with the UN on a host of issues such as Iran, Afghanistan, Lebanon or Syria, "much of the public discourse that reaches the US heartland has been largely abandoned to its loudest detractors such as (conservative radio talk show host) Rush Limbaugh and Fox News."
"Exacerbating matters is the widely held perception, even among many US allies that the US tends to hold on to maximalist positions when it could be finding middle ground," Mr Malloch Brown said.
In a furious reaction, Mr Bolton called the speech a "very grave mistake."
"We are in the process of an enormous effort to achieve substantial reform at the United Nations," he said. "To have the deputy secretary general criticise the United States in such a manner can only do great harm to the United Nations.
"Even though the target of the speech was the United States, the victim, I fear, will be the United Nations," he added. "Even worse was the condescending and patronising tone about the American people."
Mr Bolton said the only way "to mitigate the damage to the United Nations" was for Mr Annan to "personally and publicly repudiate this speech at the earliest possible opportunity."
"Otherwise I fear the consequences not just for the reform effort but for the organisation," he added.
No action against Malloch Brown
Mr Annan's spokesman Stephane Dujarric said Mr Annan "stands by the statement made by his deputy and he agrees with the thrust of it."
"So there is no question of any action being taken against the deputy secretary general," he added.
The world body faces possible financial gridlock at the end of the month if agreement is not reached on a package of management reforms.
The United States has threatened to withdraw funding if the reforms are not adopted by then, and EU countries have said they will have to take another look at their contributions.
However Mr Malloch Brown has defended his candid critique of American policy toward the United Nations, dismissing suggestions that it was anti-US or partisan.
He stressed that the speech was not intended to be "partisan or provocative" but was meant to convey the idea that "America needs a global foreign policy and the UN is a critical part of that."