The Carter administration said yesterday it has no evidence at present to support the idea that Abol Hassan Bani-Sadr's election as president of Iran will lead to the speedy release of the 50 American hostages in Tehran.

Publicly and privately, administration officials sought to damp down risking speculation that the election of Bani-Sadr, a moderate on the hostage issue, will allow the United States and Iran to strike a deal leading to the captives' freedom. They have been held since Nov. 4.

While admitting that Bani-Sadr's emergence has raised the administration's hopes for potential movement, the officials denied rumors that some new initiative is being pursued behind the secnes. If Bani-Sadr has a formula for breaking the deadlock, they asserted, it has not yet been made clear to the United States.

Instead, the officials added, the expectation is that it will take time to get a clear picture of how much strength Bani-Sadr can muster in the divided Iranian power structure and how he plans to use it in approaching the hostage question.

Summing up the administration's position publicly, State Department spokesman Hodding Carter said: "From the outset, our problem has been to find someone there in authority who is willing to negotiate with us."

But, he added, "We are unable to assess the effect of the election returns on our ability to effect the release of the hostages . . . We cannot say at this point whether Bani-Sadr will fill that bill."

In his other comments, though, the spokesman continued the administration's strategy of following a conciliatory tone, stressing U.S. support for "a democratically stable and economically progressive Iran" able to withstand the threat of "Soviet expansionism."

Most importantly, while he insisted there has been no change in President Carter's announced intention to impose economic sanctions on Iran, Hodding Carter left the impression that the sanctions are being delayed indefinitely to help strengthen the hand of those in Iran arguing for resolution of the confrontation with the United States.

Following the Soviet Union's invasion of Afghanistan last month, the administration's approach to Iran shifted from tough talk and overt pressure to arguing that Iran would best serve its interest by ending its quarrel with the United States and turning its attention to defending itself against Soviet moves.

However, on Jan. 17, a senior administration official, speaking in a press background briefing, said the U.S. sanctions plan would be put into effect "within the next few days." That intention was reiterated by President Carter in a television interview three days later.

Carter's major rival for the Democratic presidential nomination, Sen. Edward M. Kennedy (D-Mass.), seized on these statements yesterday to charge that sanctions "will only propel Iran toward the Soviet orbit" and "will do nothing to free the hostages."

Although Kennedy intended to show his divergence from administration policy, it has become increasingly evident, despite administration reluctance to say so publicly, that application of sanctions is being delayed until U.S. officials get a better idea of which way Iran might move under Bani-Sadr's increased influence.

The decision to go slow on sanctions is understood to stem from the adminstration's belief that Iranian public opinion is becoming more fearful of the Soviet Union than of the United States and that it would be unwise for Washington to take any action at this time that might provide ammunition for anti-American forces trying to reverse the trend. U.S. officials are known to feel that a majority within Iran's Islamic Revolutionary Council would like to end the confrontation with Washington by forcing a showdown with the Marxist-oriented militants holding the hostages in the American embassy compound. Until now, the council has been blocked by the support given the militants by Iran's most powerful leader, Ayatollah Ruhollah Khomeini. But, according to current U.S. analysis, even Khomeini, ailing with heart trouble and aware of the shifts in Iranian public opinion, may be willing to remove his protection from the militants and help pressure them to free the hostages.

That is why Bani-Sadr's overwhelming election is regarded as a potentially hopeful sign. He served briefly as Iran's foreign minister in the early stages of the crisis. While holding that post, he sketched the outlines of what U.S. officials since have considered, the most promising route to a solution of the impasse.

Essentially, Bani-Sadr hinted that Iran might drop its demands that deposed Shah Mohammad Reza Pahlavi be returned to stand trial as a criminal and instead settle for appointment of an international commission under United Nations auspices to investigate Iran's grievances against the shah and the United States.