The credibility of the Carter administration has been further damaged here by a recent mix-up involving King Hussein's possible visit to Washington.

Senior Jordanian officials privately describe the U.S. announcement that Hussein would visit Washington in April as "clumsy, silly and totally incomprehensible."

There are also suspicions here that the Carter administration was involved in a conspiratorial attempt to drag Jordan into the Middle East talks since it coincided with the announcement that the leaders of Israel and Egypt would come to Washington in April for a new round of peace negotiations.

The timing of the announcement proved embarrassing to Hussein since it created the impression that his talks with President Carter would be parallel to the Camp David negotiations, which Jordan had rejected.

According to both U.S. and Jordanian sources, U.S. Ambassador Nicholas Veliotes called on the king last week to inquire whether he had plans to visit Washington in April in response to an earlier invitation from Carter.

The king, according to the sources, said he had no plans for an April visit but would consider a suitable time. No specific date in April was mentioned.

The conversation took place at noon local time on the day Washington announced the planned visits of Egyptian President Anwar Sadat and Israeli Prime Minister Menachem Begin. The U.S. envoy had no knowledge of the visit by Sadat and Begin.

The Jordanians were furious when the king's Washington trip was announced simultaneously with the Begin-Sadat visits.

While the ambassador's personal integrity is not being questioned, senior Jordanian officials believe that U.S. haste to get Jordan somehow involved in the Camp David process may have been the reason for the mix-up.

These officials also wonder aloud whether the mix-up may have been caused by the same type of poor coordination attributed to the recent U.S. vote at the United Nations condemning Israel's settlement policy. Carter has subsequently disavowed the vote as a mistake.

There has been no official U.S. explanation of the Jordanian mix-up.

While Hussein has refrained from public comment, an official Jordanian statement issued two days ago was low key and in keeping with Jordan's desire to maintain friendly relations with Washington.

"We understand the disarray in Washington," one Jordanian official said privately.

Hussein's acceptance of Carter's invitation still stands, officials said, but the king will visit Washington at a "convenient time," most likely in June, when he is expected to attend the graduation of his son Abdullah from a private school.