A sudden chill developed in relations between Egypt and the United States yesterday as this country reacted with surprise and concern to remarks attributed to President Carter about the future of the occupied Arab territories and the Palestinians.

In the first such incident in many months, Foreign Minister Mohammed Kamel summoned U.S. Ambassador Hermann Eilts to demand an explanation of what Carter reportedly said. Eilts acknowledged after the meeting that the foreign minister was "disturbed and concerned."

The Cairo newspaper Al Ahram printed what it said was a "strange" interview with Carter distributed by the New York Times. The remark attributed to Carter implied approval of Israeli Prime Minister Menachem Begin's plan for limited self-rule for Arabs of the West Bank of the Jordan River and indicated that Israel would not be obliged to withdraw from all occupied Arab territories. They were interpreted by the Egyptians as a sudden American shift toward the Israeli position on these crucial issues.

Kamel asked Eilts for the text and issued a statement expressing his "deep concern over the remarks which may hurt current efforts to resolve the Middle East conflict."

Diplomatic observers said this was the first occasion in many months in which Egypt had so openly criticized Carter, whom it has regarded as sympathetic. Cairo has looked to the president for help in resolving the Middle East negotiating impasse.

According to Eyptian officials and diplomatic sources, however, it was the timing as much as the substance of Carter's remarks that upset the Egyptians. Publication of the interview followed Carter's talk with Israeli Foreign Minister Moshe Dayan and on the eve of a visit to the United States by Begin. It is also followed what is seen here as a retreat by Carter on his all-or-nothing plan to sell warplanes to Egypt and Saudi Arabia as well as Israel.

The interview, by Trude B. Feldman, quoted Carter as saying:

"My belief is that a permanent settlement will not include an independent Palestinian nation on the West Bank. My belief is that a permanent settlement will not call for complete withdrawal of Israel from occupied territories. My belief is that a permanent settlement will be based substantially upon the home rule proposal that Prime Minister Begin has put forward."

[White House press secretary Jody Powell said yesterday that Carter's statements on the three issues represented no change in the President's position. "There's nothing new to it," he said, adding that he was surprised at the Egyptian reaction.]

Feldman is a free-lance journalist based in Washington. Her interview was distributed by the feature service of The New York Times, although that paper did not print the article itself.

It is arguable whether, in fact, the president was espousing any new positions, but if quoted accurately his statement about Begin's self-rule plan for the West Bank does appear to indicate that Carter is now prepared to accept a proposal he had previously rejected.

The combination of Carter's tactical shift on the plane package and apparent diplomatic shift on the Palestinian question has raised suspicion here that the president is wavering on agreements that the Egyptians thought were firm.

Eilts met Vice President Honsy Mobarak Saturday in an effort to convince the Egyptians that Carter, accepting congressional debate on the plane sales separately instead of together, was only playing the game by congressional rules, not giving up his commitment.

But yesterday morning, the newspaper Al Gumhouria printed an editorial reliably reported to reflect official thinking. It said the shift represent "a serious retreat from the declared position of the United States and of President Carter personally."

As reported in Al Ahram, Carter said he does not favor and never has favored the creation of an independent Palestinian state in the West Bank and the Gaza Strip. Since Egypt is not pressing for the creation of such a state but only for Palestinian self-determination within a constitutional link to Jordan, Egyptian officials said they were not upset that Carter reiterated this, only by the fact he said it now.

Of more concern were Carter's reported statements on Israeli withdrawal from occupied territories and on the nature of the Palestinians' "participation in the determination of their own future," which Carter has previously endorsed.

While there was nothing new in his reported statement that U.N. Security Council Resolution 242 did not require a total Israeli withdrawal from territories occupied in 1967, Egyptian officials said they were chagrined to find no mention of the previous U.S. policy that only "minor border rectifications" were permissible.

As for the Begin proposal on autonomy for the Palestinians in the occupied territories, the foreign minister's statement noted that this proposal has already been rejected as inadequate since it would "keep the area under Israeli domination."