Dr. James C. Fletcher, newly reinstalled as NASA administrator, charged yesterday that some members of the news media "have acquired a deep and unwarranted suspicion of NASA" and that their distorted coverage could do "irreparable damage" not only to the agency and the space program but to the nation.

In a speech prepared for delivery to an aerospace industries group in Williamsburg, Va., Fletcher said the embattled National Aeronautics and Space Administration was not just "another government agency," but a symbol of American aspirations and a "vital national asset."

Acknowledging that the agency has made mistakes, he said it is "slowly but surely getting back on track" in the wake of an unprecedented string of disasters, most notably the destruction of the shuttle Challenger on Jan. 28 and the deaths of its seven crew members.

As Fletcher stressed once again the urgent need for a fourth orbiter to replace Challenger, a top White House official yesterday confirmed that President Reagan is expected to give the go-ahead for the replacement.

However, he added, a debate about how to pay for the new orbiter and additional unmanned rockets is still unresolved. He estimated the replacement shuttle would cost $2.5 billion to $3 billion.

Fletcher said NASA is "strongly resisting" the suggestion by an interagency task force of top administration officials that the extra funding come from NASA's budget.

Fletcher said in his address, "The NASA you and I know made mistakes in the past, corrected them and moved on . . . . But sometimes I wonder if the NASA you and I know is the same organization that some in the media portray since the Challenger accident."

Although most of the news media "has striven to be accurate, thorough and fair," he said, "I believe that a small number of reporters have acquired a deep and unwarranted suspicion of NASA, its organization, its motives and its people. They have sought to question every action, and to uncover its every perceived blemish and wart."

Fletcher did not name names, but criticism of the agency's management as well as its handling of information has been widespread since the accident. Members of the media and a presidential commission investigating the shuttle accident have charged that the agency, which was formerly praised for its openness, has withheld or mishandled information.

Commission Chairman William P. Rogers recently charged that NASA officials had "almost covered up" vital facts. Criticism has also come from astronauts and others in the agency.

Fletcher's remarks paralleled those made by Kennedy Space Center Director Richard G. Smith in March, accusing the commission of risking needless damage to the agency's reputation by criticizing it before the cause of the accident was known and charging that reporters had contributed to the pressure on NASA by ridiculing launch delays.

The NASA portrayed in some media accounts, Fletcher said, is "not a NASA that has done magnificent and creative things, but a NASA that has always been poorly managed, a NASA that has always made mistakes and a NASA that never got its act together . . . . I believe it creates a distorted image of who we are and what we are about."

If such coverage continues, he wondered, could it cause "public support, and thus, congressional support . . . to diminish to the point where the program itself could be in jeopardy?"

If the coverage leads to morale problems and resignations in NASA and causes it to "lose its vitality," he said, "the result could be serious damage to the United States' technological, scientific and economic leadership in the world."