Former secretary of state Henry A. Kissinger said yesterday he would not run for governor of New York in the November election, leaving the Republican Party still scrambling for a credible challenger to Gov. Mario M. Cuomo (D).

Ending a brief but intense courtship by state GOP officials, Kissinger said he was deterred by the prospect of having "to abandon all existing commitments to devote myself full time to the substance, organization and financing of an effective gubernatorial race. Circumstances do not permit this on such short notice."

One of the campaign consultants who met with Kissinger in an effort to persuade him to run said that Kissinger, who has a lucrative consulting business and busy lecture schedule, decided "he can't afford" to make the race or to serve as governor.

Now 62, Kissinger was approached by New York Republican officials who have been seeking someone strong enough to give Cuomo a serious reelection race. They paid for a poll that reportedly showed Kissinger would start far behind the governor but might exploit the "softness" in Cuomo's support.

Kissinger, who began his long career in public policy as an adviser to Nelson A. Rockefeller during Rockefeller's 14 years as governor, confirmed last week that he was considering the gubernatorial race.

With Kissinger's refusal, state Sen. Roy Goodman (R), a Manhattan liberal, is once again the leading prospective candidate. His press secretary said yesterday that Goodman "is still thinking about it," but a leading Republican campaign official in Washington said it appeared the senator was also cooling to the idea.

"I really think it's within the realm of possibility," this official said, "that we will not have anyone to oppose Cuomo."

The governor is considered a possibility for the 1988 Democratic presidential nomination and Kissinger noted in his withdrawal statement that Vice President Bush was among those who had urged him to make the race.