A heated dispute within the Carter administration over authorizing American dependents to leave Iran at U.S. government expense delayed this week's exodus of families at a time of rising anti-American sentiment in the violent protests against the shah of Iran, administration sources reported yesterday.

The administration resolved the 3-month-old dispute only this week after weighing the physical danger to Americans against the diplomatic risk of being seen as losing confidence in the shah's ability to ride out the continuing upheaval in Iran, the sources said.

The decision came at a meeting of the interagency Cabinetlevel Security Coordinating Committee, which is chaired by national security adviser Zbigniew Brzezinski, and which was attended for the first time this week by George W. Ball, former under secretary of state in the Kennedy and Johnson administrations and now acting as a temporary consultant to the National Security Council on the Persian Gulf.

White House press secretary Jody Powell said last night that he assumed that Ball had been involved in the discussion, but he could not confirm reports that Ball had helped swing the decision to move on authorizing dependents to leave Iran.

Among those strongly emphasizing the dangers of appearing to weaken the shah by giving official sanction for Americans leaving Iran in the face of trouble was the U.S. ambassador to Iran, William H. Sullivan, according to offical sources in Tehran and Washington.

But other officials here said that Sullivan carefully mixed his arguments for the strongest possible show of support for the shah with support for an evacuation plan for Americans if and when it became necessary.

Henry Precht, the Iran desk officer of the State Department, went further by categorically denying reports that Sullivan had opposed granting authorization to pay for travel by dependents who wanted to leave Iran temporarily.

The immediate center of the dispute was payment by the U.S. government for commercial airline tickets for military and embassy dependents and civilian defense employes who want to leave Iran temporarily. U.S. officials have also been updating a contingeucy plan for a total evacuation of the 41,000 Americans in Iran if the crisis deteriorates dramatically, but State Department sources emphasized that no decision has been made involving a U.S. evacuation.

While much smaller in scale and impact, the dispute over this administrative problem bore symbolic overtones similar to the bitter arguments in the Ford administration over the timing of ordering an evacuation of Saigon in 1975 as South Vietnam collapsed.

In a telephone discussion from Memphis, Powell strongly emphasized that the discussion within the administration had been over "whether you do or do not pay for these peoples' tickets" rather than over broader questions of being seen to weaken the shah.

The White House demonstrated concern over how its signals on the shah are being read earlier yesterday by moving to soften the impact of remarks by President Carter on Thursday that cast doubt on the ability of the shah to survive.

Acting on the president's instructions, State Department spokesman Hodding Carter told reporters that "the president's comments do not indicate any change in United States policy toward Iran and our support for the shah."

Asked at a breakfast meeting with reporters if he thought the shah would survive, the president responded: "I don't know. I hope so. This is something that is in the hands of the people of Iran."

Powell volunteered to reporters yesterday that the president was "quite concerned" that "erroneous interpretations" were being placed on his remarks. Powell specifically mentioned a story in yesterday's editions of The Washington Post as having upset the president.

"Any suggestion that the U.S. is changing its policy toward the shah is erroneous," Powell said.

In reporting yesterday that Carter's remarks appeared to reflect an on-going reappraisal at the White House of the close U.S. identification with the shah's regime, The Washington Post noted that "White House and State Department officials said the administration still supported the shah and that Carter's remarks did not represent any dramatic shift of U.S. policy toward Iran."

Powell failed Thursday to return a call from a reporter seeking information on the president's Iranian remarks.Asked Thursday at the noon State Department briefing about the remarks, Hodding Carter said he was unable to provide reporters guidance, because he had not seen a full transcript of the breakfast meeting discussion.

Administration sources reiterated yesterday that, while there has not been a decision to change policy on Iran, the White House does seem to take a less confident view of the shah's chances of survival and seems to be reassessing the implications of that for American policy. Even as clarified by Powell, the president's remarks seem to support this conclusion.