UNITED NATIONS, June 7 — John R. Bolton, the American ambassador to the United Nations, called on Secretary General Kofi Annan on Wednesday to repudiate “personally and publicly” the critical remarks a senior official made about the United States, but Mr. Annan turned aside the challenge.

Calling the matter “very, very grave,” Mr. Bolton said he had made the demand in a morning phone call in which he had told the secretary general, “I’ve known you since 1989, and I’m telling you this is the worst mistake by a senior U.N. official that I have seen in that entire time.”

The official, Mark Malloch Brown, the deputy secretary general, took the United States to task in a speech in New York on Tuesday, saying Washington had failed to stand up for the United Nations and had let its harshest detractors go unanswered.

Responding to Mr. Bolton on Wednesday, Mr. Annan’s spokesman, Stéphane Dujarric, said: “The secretary general stands by the deputy secretary general and agrees with the thrust of the speech. This is not a criticism of the United States; it is a call for greater U.S. involvement in the U.N.”

The showdown was provoked when Mr. Malloch Brown, a Briton, said that although the United States worked closely with the United Nations in many areas, the American public was kept in the dark about it by Washington’s tolerance of what he called “too much unchecked U.N.-bashing and stereotyping.”

Mr. Bolton seized on that assertion to say that the worst aspect of the speech was what he called Mr. Malloch Brown’s “condescending, patronizing tone about the American people.”

“Fundamentally, very sadly, this was a criticism of the American people, by an international civil servant, and it’s just illegitimate,” Mr. Bolton said. He added that “even though the target of the speech was the United States, the victim, I feel, will be the United Nations.”

The confrontation threw into blunt relief tensions between the Secretariat and Mr. Bolton, who is known for single-minded assertiveness with ambassadors and disdainful comments about the United Nations.

Mr. Malloch Brown did not mention Mr. Bolton by name, but in a critique of a working style that many diplomats associate with Mr. Bolton, he said, “The U.S. tends to hold on to maximalist positions when it could be finding middle ground.”

Mr. Malloch Brown said Wednesday that the point of his speech had not been to provoke the United States but rather to urge Washington to become more involved.

“It was a speech addressed to foreign policy makers and political leaders to say, ‘Look, you’re going to need us more than ever, therefore you have to engage to help make this institution a better institution,’ ” he said. ” ‘And you need to engage, if I dare say so, with your own public opinion to explain better why the U.N. matters to American interests.’ ”

He said he had spoken up out of concern over the polarizing effect on United Nations members of a looming showdown over a six-month budget cap that could theoretically shut down United Nations operations at the end of June.

The cap, agreed to under pressure from Washington, is generally supported by wealthy nations, which want to see reforms in the United Nations management, but is opposed by developing countries, which say such changes would diminish their power.

“This organization is slipping toward a very serious crisis,” Mr. Malloch Brown said. “We have a budget cap which expires at the end of June. We have two sides to the debate talking past each other, not engaging in finding solutions.”

The deal was originally struck to link budget approval with significant management reforms, and Mr. Bolton made frequent mention of Congressional impatience with the United Nations and legislation that would authorize Washington to withhold its dues. The United States pays 22 percent of the United Nations budget.

“It will be very hard for the Congress of the United States to understand a senior United Nations official attacking the United States government,” Mr. Bolton said in an interview.

Senator Christopher J. Dodd of Connecticut, a senior Democrat on the Senate Foreign Relations Committee, issued a statement in Washington praising Mr. Malloch Brown’s speech and faulting Mr. Bolton’s response to it.

“Mr. Bolton falls back on bullying and threats rather than constructively engaging other delegates to move reform forward,” Mr. Dodd said. “That isn’t constructive and does a disservice to United States interests at the U.N.”