President Clinton today dropped the claim of executive privilege he had invoked in the Lewinsky investigation, moving to reduce the prospect of a quick Supreme Court review in the highly charged constitutional clash between the White House and the independent counsel.

But the President continued to press the claim of a lawyer-client privilege, in an effort to limit the questioning of Bruce R. Lindsey, one of his closest confidants. And the Justice Department filed notice of its intention to appeal a lower-court ruling that ordered Secret Service officials to testify.

The abandonment of the executive-privilege claim, a step approved by Mr. Clinton at a meeting with his lawyers this morning, was an effort by the White House to narrow its appeal so as to keep the independent counsel, Kenneth W. Starr, from the rapid Supreme Court review he had sought. If the White House is successful in convincing the Supreme Court that there is no need to bypass the appellate level on the issue of attorney-client privilege, it could prolong the legal wrangling between the President and the independent counsel for many months.

Moreover, there were fresh signs today that even if Mr. Starr ultimately succeeded in defeating the attorney-client claim, he would be unlikely to gain any incriminating evidence against the President from Mr. Lindsey. In a footnote to a White House brief filed with the Supreme Court today, Administration lawyers said Mr. Lindsey, a deputy White House counsel and for three decades a close friend of Mr. Clinton, had already told Mr. Starr's grand jury that he ''had no information that anyone had committed perjury or obstruction of justice.''