NEW YORK, Dec 20 (Reuters) - With any hopes for replacing Hillary Clinton as the top U.S. diplomat dashed, Susan Rice told the annual U.N. Correspondents Association dinner "there's nowhere in the world I'd rather be tonight" - speaking against a backdrop of the State Department.

In a rare lighthearted moment, Rice made fun of her ill-fated appearance on several Sunday morning television shows in September that sparked anger among Republicans. On those shows she suggested that street protests, and not militants, were behind a Sept. 11 attack on the U.S. mission in Benghazi, Libya, in which four Americans were killed, including the U.S. envoy.

Her television remarks turned out to be incorrect and Republican critics accused Rice, the U.S. ambassador to the United Nations, of misleading the American public. She defended herself by saying her remarks had been cleared by U.S. intelligence agencies beforehand.

"My talking points for this evening have been provided to me and fully cleared by the intelligence community, so how could this possibly go wrong?" Rice told a New York audience of 540 on Wednesday that included Hollywood actor and former California governor Arnold Schwarzenegger and U.N. chief Ban Ki-moon.

Rice withdrew her candidacy for the post of secretary of state last week, saying the Senate confirmation hearings would have been overly contentious.

The 48-year-old diplomat, who has a reputation for bluntness and caustic language during closed-door negotiations of the U.N. Security Council, also made fun of her diplomatic dust-ups with Russian envoy Vitaly Churkin, who has criticized her vocabulary.

To have a dig at Churkin, she recalled the oft-ridiculed remark of former Alaska governor and 2008 Republican vice-presidential candidate Sarah Palin that she could see Russia from Alaska.

"Day after day, I engage in highly substantive, highly technical negotiations with my colleagues here at the U.N., like the Russians," Rice said. "As a matter of fact, I can see the Russian mission from my house." (Reporting By Louis Charbonneau and Michelle Nichols; Editing by Vicki Allen)

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