United Nations Ambassador Jeane J. Kirkpatrick yesterday blamed a communications breakdown--not her running conflict with Secretary of State Alexander M. Haig Jr.--for her failure to vote the official U.S. position on a proposed cease-fire for the Falkland Islands.

In an appearance on "Meet the Press" (NBC, WRC), Kirkpatrick joined other administration officials in seeking to downplay her much-publicized conflicts with Haig as a factor in the embarrassing mix-up.

She denied that she and Haig are not on speaking terms. "Do we talk to each other? Yes," she said, adding that she spoke to Haig by telephone twice during the 24 hours before the vote.

But the enduring friction was evident in several of Kirkpatrick's comments. She said she and Haig were not communicating directly at the time he decided to switch the U.S. position. Her aides were in touch with Haig only via the State Department, which had an "open wire" to Haig at the economic summit in Paris, she said.

Kirkpatrick said she tried to check with Haig once more before casting her vote, but did not receive his response in time.

Haig defended the indirect hook-up by calling Kirkpatrick a "company commander" and saying: "You don't talk to a company commander when you have a corps in between."

Asked to comment on this characterization, Kirkpatrick responded with icy restraint.

Such military terms, she said, "may be more meaningful to Secretary Haig who is after all a general than they are to me who am a professor in my ordinary life." She added that "armies are very hierarchical and universities are very informal, egalitarian places which don't attach much importance to titles."

White House chief of staff James A. Baker III, appearing on "Face the Nation" (CBS, WDVM), also sought to minimize the conflict between Haig and Kirkpatrick, calling the problem "simply a communications snafu. It's unfortunate but it's one of those things that's going to happen from time to time."

Baker said he did not believe the mix-up would weaken the U.S. position in the United Nations, nor would it hurt the stature of Kirkpatrick or Haig.

"The president has great confidence in Ambassador Kirkpatrick's ability . . . just as he has with respect to Secretary Haig," Baker said.

Kirkpatrick said she received Haig's instructions to abstain from a vote on the controversial resolution "about three to five minutes too late, and in the U.N., of course, you can't change a vote."

She said her "no" vote on the resolution represented what had until those last minutes been the U.S. position, and she believed she was following White House wishes.

Some officials with President Reagan and Haig in Europe--where the White House is attempting to foster an image of competence and cohesiveness in the administration--criticized Kirkpatrick for drawing attention to the confusion.

But Kirkpatrick said she acted in accordance with the State Department's wishes.

"I was instructed to vote no and then I was instructed to abstain and I explained you couldn't change a vote. Then I was instructed to explain that if we could change our vote we would abstain," she said. "I did all those things. I acted as an instructed representative throughout."

The confusion over the U.N. vote reportedly incensed both British and Argentine officials.

The British, who firmly opposed the resolution and had expected the United States to vote against it, were upset about the attempt to abstain. The Argentines were upset over the vote itself, administration officials said.

Kirkpatrick had lobbied from the start for an abstention rather than a "no" vote on the resolution, saying she feared that U.S. relations with Latin America could suffer from too close an identification with British interests.