Mayor Jane Byrne today endorsed the reelection of President Carter. Or did she?

With Rosalynn Carter at her side, Byrne said "yes, I am" when reporters asked if she was going to endorse Carter. The First Lady was in Chicago for a Columbus Day parade.

There appeared to be disagreement, however, over whether Byrne -- who frequently has engaged in repartee with journalists only to retract her words later -- actually meant what she said.

Responding to further questions, Byrne said that she thought the Cook County Democratic Central Committee would hold a caucus "and I think we'll come out and endorse him."

Byrne's pro-Carter comments, coming after she praised the president at an O'Hare airport news conference for his "great record," was especially surprising because the mayor is considered by many political observers to be leaning toward supporting a presidential campaign by Sen. Edward M. Kennedy (D-Mass.).

Until today, Byrne successfully had ducked questions about her presidential preferences.

Mrs. Carter's press secretary, Mary Hoyt, told reporters that Byrne's remarks were "a very strong statement for President Carter."

Byrne's press secretary, Michael Sneed, confirmed the mayor's statement but refused to "interpret" it.

The issue may be settled Monday when the president is to fly here to address Byrne's $100-a-plate fund-raising dinner.