Jeane J. Kirkpatrick, the former U.S. ambassador to the United Nations, said yesterday she will not seek the Republican nomination for president in 1988.

In a statement, Kirkpatrick said: "I've carefully considered this issue, and firmly decided for personal and political reasons not to seek the Republican nomination. Naturally, I'm grateful for the confidence of those who urged me to become a candidate."

Kirkpatrick made the decision after discussing it with advisers at her Bethesda home, according to her spokesman, David Carmen.

It had been widely believed that her candidacy would be a blow to Rep. Jack Kemp (R-N.Y.), who is trying to unite conservatives behind his bid.

Kemp, Vice President Bush, former Delaware governor Pierre S. (Pete) du Pont IV, former secretary of State Alexander M. Haig Jr. and former television evangelist Marion G. (Pat) Robertson have entered the race. Senate Minority Leader Robert J. Dole (R-Kan.) has said he will declare his candidacy Nov. 9.

Kirkpatrick was a Democrat when Reagan, attracted to her tough foreign policy views, named her as his first ambassador to the United Nations.

Kirkpatrick, 60, served slightly more than four years as ambassador and earned a reputation as a hard-line anticommunist whose strong views put her in conflict with her administration colleagues as often as with fellow U.N. diplomats.

But many conservatives admired her views and urged that she be named secretary of state or national security adviser. President Reagan rejected their entreaties and in April 1985, Kirkpatrick returned to Georgetown University.

Immediately after leaving her U.N. post, Kirkpatrick formally changed her voter registration from Democrat to Republican.