Senate Majority Leader Howard H. Baker Jr. and Minority Leader Robert C. Byrd met with FBI Director William H. Webster and Attorney General William French Smith yesterday to discuss "institutional" flaws that may have been revealed in the confirmation proceedings of Labor Secretary Raymond J. Donovan.

In the one-hour discussion on Capitol Hill about the manner in which top officials are confirmed by the Senate, Smith and Webster held the White House responsible for any information withheld from the senators, according to a Senate leadership aide.

"The FBI makes it clear it is not their responsibility to supply the materials directly to the Senate. It is the White House," the aide said.

Asked by the senators for a clarification of who the FBI works for in these proceedings, Webster and Smith reportedly responded that currently and historically it is the White House, and that there are no written guidelines for the FBI as to how they should be conducted.

The Senate is waiting for a White House response to Byrd's request Wednesday that all material on Donovan provided by the FBI to the administration but withheld from the Senate be turned over to the Senate. Byrd's request also included any such information concerning all other administration officials confirmed by the Senate.

Both senators also reportedly asked that the FBI "vigorously pursue" its investigation of the counter-investigation of Senate staff members by Donovan's former business, Schiavone Construction Co. of Seacaucus, N.J., and supply the senators with periodic reports.

Parts of the discussion were too "sensitive" to be revealed yet, but will "be followed up on," the aide said.

Donovan was the subject of a six-month investigation by a special prosecutor whose report was released Monday. The report found "insufficient credible evidence" to indict the labor secretary on charges that he had links to organized crime and had been involved in corrupt labor practices.

Yesterday's meeting took place at the request of Senate Labor Committee Chairman Orrin G. Hatch (R-Utah) and Sen. Edward M. Kennedy (D-Mass.), the ranking minority member, who have been prime movers in pursuing the Donovan charges.

The meeting involved some "dancing around" but it was felt that the administration officials were "basically cooperative," the aide said.