Britain and the United States today vetoed a Security Council resolution asking an immediate end to the fighting in the Falklands. Britain said the text lacked a sufficiently specific link between a cease-fire and unilateral Argentine withdrawal.

Only moments after the voting, however, U.S. Ambassador Jeane J. Kirkpatrick was handed a small piece of paper by an aide as she was explaining the U.S. veto. Shortly afterward, she stunned the council by saying, "I am told that it is impossible for a government to change a vote after it is cast. But I have been requested by my government to record the fact that were it possible to change our vote, we should like to change it from a veto, a no, that is, to an abstention."

The statement left both the British and the Latin Americans startled, and Kirkpatrick turned in her chair as she finished her statement to face the British ambassador, Sir Anthony Parsons, lifting her arms in a shrug of bewilderment.

She also seemed stunned by the abrupt change herself, telling puzzled reporters after the meeting: "You don't understand? I don't understand either."

Kirkpatrick herself is known to have expressed misgivings about the impact of a veto on U.S. relations with Latin America. Just before announcing that the United States would have preferred to abstain, she spoke of the "clash of values and loyalties" that went on within the administration "all the way down to the actual vote."

Kirkpatrick said that she had received her original instructions to veto the resolution this morning from Deputy Secretary of State Walter Stoessel and Assistant Secretary Thomas O. Enders in Washington. But later in the day, she said, it became clear to her that Britain was refusing to accept certain amendments she considered reasonable.

She sent this information to Secretary of State Alexander M. Haig Jr., who is attending the economic summit in Paris, but did not receive instructions from Haig to abstain rather than veto until after she had voted, Kirkpatrick said.

[The State Department later issued a statement saying, "The defects in the resolution, while substantial, did not justify a 'no' vote," United Press International reported.]

Nine nations--the Soviet Union, Poland, China, Panama, Spain, Ireland, Japan, Zaire and Uganda--voted for the resolution. France, Togo, Guyana and Jordan abstained. Negotiations on a compromise text broke down this afternoon.

Argentine negotiator Brig. Gen. Jose Miret told reporters he had insisted on a British withdrawal from the Falklands to start 48 hours after Argentine withdrawal began, a demand unacceptable to Britain.

Parsons said the main problem was the lack of an "inseparable link between the cease-fire and immediate Argentine withdrawal within a fixed time limit."