Current U.S. Ambassador John Bolton asked for a moment of silence at a senior staff meeting of the U.S. mission to the United Nations on Friday.
Kirkpatrick began her public life as a Hubert Humphrey Democrat, but switched to the GOP in 1985 and became a proponent of Reagan era conservatism, serving in his administration as a member of his Cabinet and National Security Council.
During the Reagan years, she played a quiet role in cutting off U.S. aid to a leftist government in Nicaragua and supporting a military junta in El Salvador.
The often blunt Kirkpatrick was a steadfast supporter of Israel in the United Nations, where the Jewish state was often denounced.
Prior to her appointment to the United Nations in 1981, she was a political science professor at Georgetown University, starting in 1957.
For her work in the government, Kirkpatrick was awarded the Medal of Freedom -- the nation's highest civilian honor -- in 1985.
Kirkpatrick remained involved in public issues even though she left government service 20 years ago. She was a senior fellow at the conservative think tank American Enterprise Institute.
She joined other former U.N. ambassadors in writing Congress in 2005 to say its plan of withholding dues to the world body in order to force reform was misguided and would "create resentment, build animosity and actually strengthen opponents of reform."
"I think she spoke clearly for liberty in the world," Bolton said, reported the Associated Press.
Senate Majority Leader Bill Frist, R-Tenn., said Kirkpatrick "stood up for the interests of America while at the U.N., lent a powerful moral voice to the Reagan foreign policy and has been a source of wise counsel to our nation since leaving the government two decades ago. She will be greatly missed."
Kirkpatrick's health had been in decline recently and she was "basically confined to her house," going to work about once a week and then less frequently, according to her assistant Andrea Harrington, the AP reported.