President Carter yesterday directly disputed Israeli Prime Minister Menachem Begin's version of what was and was not agreed to at the Camp David summit conference on the issue of future Jewish settlements along the West Bank of the Jordan River.

Commenting publicly for the first time on the dispute, Carter said he had "a very clear understanding" with Begin that the question of new settlements would be settled by negotiations during a five-year transitional period during which the "final status" of the Israeli-occupied West Bank is to be decided.

He warned that "a very serious problem will be created if Begin continues to assert that he agreed to a moratorium on new Jewish settlements only during the period of negotiations over a separate Egyptian Israeli peace treaty, a process scheduled to take up to three months.

The Middle East was the dominant topic during Carter's one-hour breakfast interview with a group of reporters at the White House. He also predicted that the State Department will grant a tourist visa to Rhodesian Prime Minister Ian Smith, who has applied for permission to visit the United States.

Such a tactic, Carter noted, would not imply that the United States is ready to grant diplomatic recognition to Rhodesia.

Confirming that he made what he considered "a good tradoff" by dropping a demand that existing Israeli settlements not be expanded in return for Begin's agreement to an effective five-year moratorium on the new settlements, the president said.

"I don't think there is any doubt about the language . . . Begin's recollection is that he would let me know the following day. That was not the recollection of us because it was an important item."

Carter added, "My belief is that Begin did agree not to start any new settlements during the time the negotiations on the West Bank-Gaza self-government were being conducted, and that the status of the future settlements would be determined by the negotiations."

The issue of new West Bank settlements was deleted from the framework for a comprehensive Middle East peace reached at the Camp David summit. The issue was to be settled in a letter from Begin to Carter, but the letter has been held up because of the conflicting versions of the understanding reached at the summit.

The U.S. position, in effect, would impose a five-year freeze on new settlements because it would subject new settlements to a veto by other parties to the negotiations, including local West Bank Palestinians.

On other topics during the interview, the president:

Reasserted his determination to obtain a new strategic arms limitation talks (SALT) agreement with the Soviet Union soon and to submit it to the Senate for approval "quite early next year," if possible. He said he expects to meet with Soviet Leader Leonid I. Brezhnev, possibly in Hawaii or Alaska, when a SALT accord is near.

Predicted that the Camp David success will strengthen him in dealing with other issues and produce a perception that "I am more to be trusted on making difficult decisions on international affairs than before."

Said he believes the "taxpayers' revolt" is directed at local property taxes and not federal income taxes.

Carter also indicated that, except for some health measures, he plans no major new legislative initiatives next year.