President Reagan rejected suggestions Friday that Attorney General Edwin Meese should resign, despite a direct warning the attorney general has severe legal problems.

Officials confirmed that Reagan met privately with the attorney general earlier this week after discussing with two top-echelon Meese aides why they quit amid publicity over a long-running criminal investigation of Meese.An administration source confirmed that one of the two William Weld, who resigned as head of the department's criminal division told the president that, had he been running the probe, he would have sought indictment of Meese.

But Reagan brushed aside a question about whether Meese should resign with a simple "no" Friday and also answered "no" when asked whether Meese a longtime friend and key aide has offered to quit.

Meese, under investigation on several fronts by a special prosecutor, has steadfastly insisted he has done nothing wrong, and Justice Department spokesman Patrick Korten said the attorney general has "absolutely" no intention of resigning.

Korten confirmed that Meese met with Reagan on Wednesday after the president talked with Deputy Attorney General Arnold Burns, the No. 2 man at Justice, and Weld. They abruptly resigned March 29 and sources said their reason was concern over Meese's legal problems and a lack of leadership.

As Burns was leaving his office for the last time Friday, he declined to provide details of the Wednesday meeting, saying it would be "inappropriate" to comment.

But asked whether the president had accepted his advice, Burns said, "Not at all. I really don't know what the president is or is not going do."

"It was a very, very frank exchange of ideas that we had with him (Reagan)," Burns added. "He's got to make his decision in his way, in his own time."

With Burns and Weld and a number of their top aides either gone or leaving, roughly a dozen top Justice Department jobs are open. Some officials have said the agency has been severely hampered by the leadership vacuum, although Meese maintains the department is operating without a hitch.

Reagan, when asked how the agency is operating, replied, "Just fine.

Late Friday afternoon, the White House announced that Reagan is nominating Treasury Department official Francis Keating to succeed Stephen Trott as associate attorney general, the department's No. 3 post. Trott resigned earlier to become a federal appeals court judge.

Meese, however, has not been able to find a replacement for Burns as No. 2 his latest choice, St. Louis lawyer John Shepherd, withdrew his name Wednesday citing unexpected "pressure" on him and his family due to his selection.

Independent counsel James McKay has been investigating Meese for nearly a year in connection with Meese's conduct in serveral matters, including his involvement with the scandal-ridden Wedtech Corp.

And McKay's federal grand jury has heard testimony from Meese and his wife, Ursula, over the financing of her public service job.