UNITED NATIONS — As America’s ambassador to the United Nations bowed out yesterday after a stint that left no one at Turtle Bay indifferent, and as President Bush said he was “deeply disappointed” with the senators who blocked John Bolton’s renomination, many among the United Nations’s outgoing leadership team could hardly disguise their glee.

Even some of the strongest advocates of strong ties between America and the United Nations said that regardless of Mr. Bush’s choice of replacement, the hardships that marked Mr. Bolton’s 17-month tenure are not going away.

“After careful consideration, I have concluded that my services in your administration should end when the current recess appointment expires,” Mr. Bolton wrote to Mr. Bush on Friday, after deliberating with his strongest Washington ally, Vice President Cheney.

Mr. Bolton’s decision follows the resignation of one of Mr. Bush’s top hawkish supporters, Defense Secretary Rumsfeld, and as Democrats are gearing up to assume power in both houses of Congress. It also comes during the last month of Secretary-General Annan’s 10-year term, and a week before South Korea’s Ban Ki-moon takes the oath of office.

Mr. Bolton, an outspoken critic of Mr. Annan’s administration, was one of Mr. Ban’s earliest supporters and, according to aides to both, held many recent meetings with the incoming secretary-general, as Mr. Ban works to shape Turtle Bay’s new leadership.

“With a new secretary-general and a new Congress, there’s a possibility of a new beginning here, so I think whoever comes in” as American ambassador “has a chance to have a honeymoon period,” a frequent critic of Messrs. Bolton and Annan, professor Edward Luck of Columbia University, told The New York Sun.

Mr. Luck, who said he hoped the incoming American ambassador could “stop the bleeding” in Washington’s relations with the United Nations, is a strong candidate to become the top American in Mr. Ban’s inner Cabinet. “I’ve done some speech writing for him,” he said yesterday. “We talked about doing something for him.”

The American ambassador in Iraq, Zalmay Khalilzad, a leading candidate to replace Mr. Bolton, is said by some of his confidants to be “very interested” in the position. Other possible candidates include the undersecretary of state for democracy and global affairs, Paula Dobriansky; a former Senate majority leader, George Mitchell, and Rep. Jim Leach, a Republican of Iowa, who lost his seat in the last election.

Mr. Bush made clear yesterday, however, that his preferred choice would have been Mr. Bolton, and that only the “shallow politics of the Senate” prevented his reconfirmation. “The reason why I think he deserved to be confirmed is because I know he did a fabulous job for the country,” Mr. Bush said at the White House, alongside Mr. Bolton.

Democratic critics, meanwhile, expressed the hope yesterday that the next ambassador would be more agreeable to his Turtle Bay colleagues, as well as to Washington critics of Mr. Bush’s policies.

“With the Middle East on the verge of chaos and the nuclear threats from Iran and North Korea increasing, we need a United Nations ambassador who has the full support of Congress and can help rally the international community to tackle the serious threats we face,” Senator Kerry, a Democrat of Massachusetts, said.

Mr. Bolton’s strongest Turtle Bay opponent, Deputy Secretary-General Mark Malloch Brown, was unable to completely hide his satisfaction yesterday. “No comment,” he told reporters, adding, “and you can say he said it with a smile.”

Earlier this year, Mr. Malloch Brown’s benefactor, financier George Soros, backed an anti-Bolton advertising campaign in New Hampshire. An outgoing senator from the state, Lincoln Chafee, ended up being the lone Republican on the Foreign Relations Committee who opposed Mr. Bolton’s nomination, effectively blocking a vote by the full Senate.

“A handful of United States senators prevented Ambassador Bolton from receiving the up or down vote he deserved in the Senate,” Mr. Bush said in a statement, “They chose to obstruct his confirmation, even though he enjoys majority support in the Senate, and even though their tactics will disrupt our diplomatic work at a sensitive and important time.”

Mr. Bolton’s toughest Washington and Turtle Bay critics said he was too plainspoken and that he preferred forcing America’s will on others instead of seeking consensus.

“I think Ambassador Bolton did the job he was expected to do,” Mr. Annan told reporters yesterday, adding however: “What I have always maintained is that it is important that the ambassadors work together.”

India’s ambassador, Nirupam Sen, a leading voice in a dominant General Assembly voting bloc that has often clashed with Mr. Bolton, said, however, that Mr. Bolton’s “very frank, very firm” style “made it easier in a sense. It made it more difficult for some. It made it easier for us, because we knew exactly what his position was.”

For Mr. Luck, many of the issues that underlined Mr. Bolton’s clashes with the General Assembly were partially Mr. Bolton’s tendency to “shoot himself in the foot,” but also a product of an uneasy period in Washington’s relations with Turtle Bay. “Even if Bolton had been the perfect emissary for the U.S.,we were going to have a difficult time,” he said.