President Carter yesterday flatly rejected congressional demands for the ouster of Energy Secretary James R. Schlesinger, saying Schlesinger has his "full trust and confidence."

Carter's statement came in a letter, dated Wednesday and made public by the White House yesterday, to Sen. Dennis DeConcini (D-Ariz.). It was a reply to a letter from DeConcini calling for Schlesinger's resignation.

"While I welcome your views and recognize that the administration of the Department of Energy can always be improved, I continue to have full trust and confidence in Secretary James Schlesinger," the president wrote.

Beneath his signature, Carter added a handwritten note. "He [Schlesinger] has a very difficult job and needs all the help and support he can get," the note said. "He's got mine."

Bob Maynes, DeConcini's press secretary, said the Arizona Democrat had not received Carter's letter at the time it was made public by the White House. He quoted DeConcini as saying, "I admire the president's sense of loyalty, but I believe he has picked the wrong general to direct what he has termed 'the moral equivalent of war.'"

Schlesinger, who has often been accused of arrogance and poor political judgment, has never been a popular figure on Capitol Hill. On Tuesday, during a hearing in which Schlesinger testified, Sen. John A. Durkin (D-N.H.) called for the energy secretary's resignation. The next day, in statements on the Senate floor, Durkin was joined in the same request by DeConcini and five other Democrats.

It is doubtful that any of the senators expected a Schlesinger resignation to follow their request, given the president's record of loyalty to his top appointees. Carter was lavish in his praise of each of his Cabinet secretaries when he appointed them. Despite the criticism of some Cabinet secretaries by White House officials, the original Carter Cabinet remains intact after more than two years, highly unusual in recent history.

Moreover, while the president has enlarged his White House staff, his core of senior assistants has remained constant, another sign of his unwillingness to consider outside criticism of his choice of advisers.

In his letter to Carter, DeConcini accused Schlesinger of being "a major cause" of the administration's failure to develop a "true energy policy" or to convince the public that such a policy is needed.

"Unquestionably, Mr. Schlesinger is a fine man and a dedicated public official," DeConcini wrote. "However, he is quite simply the wrong man for the job. I believe that an effective secretary of energy must enjoy the confidence of the Congress and the public. Mr. Schlesinger appears to enjoy neither."

White House officials appeared anxious to respond to these and other criticisms of Schlesinger yesterday. In response to a question about the energy secretary's standing in the administration, White House press secretary Jody Powell said Schlesinger has Carter's "complete confidence" and volunteered to make the letter to DeConcini public.