Saudi Arabia's Crown Prince Fahd has put off a mid-March visit to Washington, leaving U.S. officials uncertain about whether the postponement was due to health or to a "diplomatic illness" prompted by growing coolness toward the Carter administration.

Because the U.S.-Saudi relationship is such an important element of the administration's foreign policy, Fahd's action touched off considerable speculation in diplomatic circles about what caused his sudden reluctance to come here.

Adding to the confusion was a glaring discrepancy in the explanations given yesterday by the U.S. and Saudi governments for putting off the March 13-14 official visit.

White House and State Department spokesmen said Fahd sought the post-ponement because of health problems that might require him to take hospital tests.

But an official Saudi announcement made no mention of health problems and said the visit was being postponed "through the mutual agreement of the two governments in order to provide the time needed for a study of the issues of mutual concern" to be discussed by Fahd and President Carter.

Washington's ties with the Saudi monarchy are regarded as especially sensitive at this time because of the disruption that Iran's internal turmoil has caused in the Middle Eastern oil supply and because of U.S. efforts to push an Egyptian-Israeli peace treaty to completion.

Despite persistent efforts by the administration, the Saudis have refused to endorse the Egyptian-Israeli negotiations or the other elements of the Camp David framework for a Middle East peace. There also have been increasing signs of Saudi unhappiness at U.S. oil policy and disappointment at U.S. inability to do anything about the events that toppled the pro-western government of the shah of Iran.

For these reasons, there was an immediate tendency in diplomatic circles to view postponement of Fahd's visit, which had been sought eagerly by the White House, as a Saudi attempt to keep Washington at arms length for the time being.

That interpretation was publicly denied by the administration yesterday. Tom Reston, a State Department spokesman, said that while the two countries have occasional differences, "we do not agree with press stories that there are strains in our relations."

In private, though, administration sources conceded that they could not say for certain what prompted the Saudi action. The sources said the Saudi request for a postponement was made last weekend on grounds that Fahd had some medical problems and that U.S. officials initially had accepted that explanation at face value.

As a result, the sources added, the administration was left puzzled and embarrassed by the Saudi government's failure to cite medical reasons in its statement. As of late yesterday, the sources said, two theories were being advanced privately by administration policymakers to explain the Saudi conduct.

According to one theory, they said, Fahd, who is regarded as the real power behind King Khalid, is ill but unwilling to advertise it publicly at a time the Middle East is being swept by unrest and agitation against the region's more feudal governments.

The sources said the other, more widely held, theory is that the visit was postponed for political reasons -- although not of a type that U.S. officials regard as potentially disruptive to long-range relations between the two countries.

Specifically, they said, the apparent reason rests with the Egyptian-Israeli ministerial talks being held at Camp David under Secretary of State Cyrus R. Vance's mediation in an effort to break the deadlocked treaty negotiations.

Although the Camp David talks are expected to be recessed in a few days, there is a strong chance they will be resumed next month. Since Saudi Arabia continues to keep its distance from the Camp David process, the sources said, it is likely that Fahd didn't want to be in Washington at the same time as the talks or even within a time so close it might imply Saudi approval of the Egyptian-Israeli negotiations.

In a related Middle East development yesterday, administration sources said they had no information to support unofficial reports from Cairo that several hundred Egyptian soldiers have been sent to Oman to replace Iranian troops that had been helping to protect the sultanate before their withdrawal early this month.

The reports had attracted especially wide attention because of increasing signs that Egyptian President Anwar Sadat, concerned about events in lran, has been weighing plans for his country to play a larger military stabilizing role in Middle Eastern countries threatened by aggression or internal unrest.