White House national security adviser Richard V. Allen decided without consulting his superiors to appear on "Meet the Press" (NBC, WRC) Sunday, according to a statement released by the White House today.

Allen "has advised the White House of the invitation and his decision to accept it," the statement said. President Reagan, who is vacationing at his ranch 20 miles north of here, was reported to be aware of Allen's decision.

In recent days, Allen has mounted what one White House official calls a counteroffensive against the allegations concerning his acceptance from Japanese journalists of $1,000 in cash which he left in a safe for eight months, the terms of the sale of his consulting business and his continuing contacts with former clients after taking his White House post.

Allen's superiors have let Allen handle his defense. He has been permitted to make statements and answer questions as he chooses, but the White House has made clear that it is not putting its imprimatur on the exchanges that have taken place between reporters and Allen.

The White House statement today said Allen had been invited directly by NBC, making it clear that the invitation had not been passed through any White House official or solicited by any of Allen's associates.

Allen's counteroffensive has included a statement by Navy Secretary John Lehman, a friend of Allen's, that Allen told him about the $1,000 in cash long before it was found in a National Security Council safe in mid-September.

The purport of Lehman's statement was that any person planning to make personal use of cash would not tell others of its existence. Allen says he took the cash from Japanese journalists who had interviewed Mrs. Reagan Jan. 21 in order not to embarrass the Japanese by refusing what was offered as a thank-you payment. He says he planned to turn the money over to the proper government authorities but forgot about it.

Chizuko Takase, who handed Allen the money and who is the wife of a longtime Allen friend and business associate, came forward this week to say that she had discussed the thank-you gift with Allen in advance of the interview and he had made it clear that he did not want any payment. The money was to go to charity, she said. Mrs. Reagan was ignorant of the thank-you gift, according to her spokeswoman, Sheila Tate.

Allen's secretary, Irene Derus, also spoke up this week and confirmed that Allen had given her the money to put in a safe while making it clear that he wanted it turned over to government authorities. She also forgot about it, she said.

Allen, who had been refusing to give interviews, joined the counteroffensive himself by talking to The New York Times to deny angrily that there is any conflict of interest in the fact that he is receiving monthly payments from the sale of his consulting firm, Potomac International Corp., while meeting from time to time with clients of the firm.

His appearance on "Meet the Press," however, will be the most dramatic effort by Allen to clear the air. It comes while the White House is still taking the official position that it would be inappropriate for any of its officials from the president on down to comment on the case because of the ongoing Justice Department investigation.