Attorney General William French Smith said yesterday Senate leaders should obtain background information on presidential appointees from the White House and not the FBI.

The FBI has come under heavy criticism from the Senate in recent weeks because of its failure to pass along allegations of ties between Labor Secretary Raymond J. Donovan and organized-crime figures to the Senate Labor Committee during confirmation hearings early last year.

The information had been turned over to the White House immediately after Donovan's background check. A special federal prosecutor closed the Donovan case last month, citing insufficient credible evidence.

Smith, in a breakfast meeting with reporters, said that the FBI felt "caught in the middle" on the Donovan case because their assignment in the past has been to provide the background information to the White House, not to Congress, to help the president choose his Cabinet and other high-level positions.

FBI Director William H. Webster "has asked us to look into . . . the role of the FBI in what is referred to as spin investigations. We . . . are responding to that request," Smith said.

He also said that the Justice Department, at Webster's request, was considering changing or at least clarifying the process by which the FBI investigates high-level presidential appointees.

"What the FBI has been asked to do in the past is to provide information to the White House with respect to appointees . . . . As a result of what has happened recently, the appearance has been that really the function of the FBI . . . was to run a whole criminal investigation and report the results to Congress--which is not the basis under which the whole process has been undertaken since the days of Harry Truman," Smith said.

Smith said the review would clarify just how far the routine background inquiries should be carried.

In the Donovan case, Smith said the FBI was originally asked to do a background check in a five-day period over the New Year's holiday weekend.

"The kind of thing the FBI can come up with under those circumstances is vastly different from what it could come up with if they were undertaking a major investigation by criminal standards," he said.

"I think what Director Webster wants is an understanding by everybody what that assignment is and to whom he is to report so that he doesn't get caught in the middle with a situation that gives the impression that whatever he does should be sent to Congress or a congressional committee or whatever," Smith said..

Smith said he was still "evaluating" a "highly unusual" request by Senate Democrats two weeks ago that he turn over to them information the FBI provided to the White House in background checks on all of President Reagan appointees confirmed by the Senate.

In response to questions, Smith also discussed his decision in May to return a controversial $50,000 severance fee that he accepted just before taking office, and to limit tax deductions on two oil and gas drilling projects to his actual investment.

"I did what I did on the tax writeoff really just to turn the subject off. Had it not been for the fact that it was becoming what you call a political issue . . . with our friend Sen. Edward M. Kennedy jumping into the act . . . I never would have done that. The same thing is true with the $50,000. I did that just to turn the subject off," he said.

"In my opinion, totally unjustifiably, it had reached the point where it was becoming a political issue that could develop into far more than the facts actually warranted," Smith said.

Smith refused to comment directly on the ongoing investigation of illicit sexual activity and drug use on Capitol Hill, but he said the Justice Department had not ruled out prosecuting members of Congress if there were evidence illegal drug use.

Smith said, "Getting the dealer is better than getting a user, but that does not mean that what the law says is a violation is not a violation. . . .

"We have to allocate the resources as best we can," he said. "That does not mean we are saying that people in that category are not violating the law. . . . We are not able to prosecute everybody. That does not mean that in a given circumstance we might not."