The White House gave tacit approval yesterday to the Defense Department's decision to have officials take lie-detector tests in its search for a news leaker, but it said the Agriculture Department has gone too far in its media crackdown.

Deputy press secretary Larry Speakes said the White House regarded the use of lie detectors at the Pentagon as "an internal Department of Defense matter."

"I would assume that if the president objected, he would take it up" with Defense Secretary Caspar W. Weinberger, Speakes said.

Frank C. Carlucci, deputy defense secretary, voluntarily took the first lie-detector test the other day to prove that he was not the person who leaked a budget projection figure to a reporter. Defense Department officials say the tests are now being given to other Pentagon officials.

Over at the Department of Agriculture, concerns are about parity, not weaponry.

Agriculture's senior officials received a memo the other day from the department's press secretary explaining that the White House would be coordinating all major media appearances--"including print interviews."

But Speakes said that the White House--even as it is in the midst of its new get-tough policy on leaks and interviews--does not want to go quite that far.

"I think there has been a large amount of confusion here between classified information and the coordination of major television appearances," Speakes said.

The White House wants to coordinate appearances by administration officials on television talk and interview shows to avoid duplication, he said; it has not asked agencies to coordinate interviews of officials with newspaper and magazine reporters.

Agriculture's deputy press secretary, David Lane, said the memo was written by his boss, John Ochs, who is now traveling in Africa with Secretary John R. Block.

Lane said he did not know if Agriculture would now ease its policy. "Our rules might be different than the White House's," he said. "There's nothing that prohibits us from being more restrictive, if you want to put it that way."