WASHINGTON (AP)—In a move that reportedly shocked Attorney General Edwin Meese III, the Justice Department’s No. 2 official and the head of the department’s criminal division both abruptly resigned Tuesday amid a nearly year-old criminal investigation of Meese.

Deputy Attorney General Arnold Burns said in a letter to President Reagan that “Unfortunately, I have regretfully concluded that I must return to private life at this time.” He did not elaborate.

William Weld, who as an assistant attorney general oversees all federal criminal investigations, resigned effective at the close of the business day Tuesday, despite a personal plea from other department officials that he remain for several weeks.

Two of Burns’ aides and two of Weld’s aides also quit simultaneously.

The decision by Burns and Weld, who refused to say why they are resigning or to discuss their plans, leaves a gaping hole in the leadership of the Justice Department.

Meese’s continuing legal problems have “everything to do with” why the two men quit, said a department source familiar with the reasons for the resignations who spoke on condition of anonymity.

The unexpected resignations were the result of the fact that “major things aren’t getting done at the Justice Department, nothing’s moving because Meese is under this cloud,” said another informed department source.

Meese first learned the two would step down when Burns and Weld walked into the attorney general’s office at 8 a.m. Tuesday and informed him of their decisions.

The two men conveyed to Meese the sentiment that “it’s nothing against you personally, Ed,” but “we want to go home,” said one department source familiar with the discussion. Several department sources characterized Meese as “absolutely shocked” by the decision.

Meese’s chief spokesman, Terry Eastland, said the attorney general “expressed appreciation for the job these two men have done” and “wished them well in their future endeavors.” Both had served in their current jobs since Oct. 17, 1986.

White House spokesman Marlin Fitzwater said President Reagan accepted the resignations “with regret” and thanked Burns and Weld for serving “with distinction.”

Fitzwater said Reagan continues to have “full confidence” in Meese and the Justice Department and that the resignations did not cause any particular concern among the president and his advisers. “We have people resigning all the time, especially late in the administration,” he said.

Meese has been under investigation for nearly 11 months by independent counsel James McKay, who last May 11 began looking into Meese’s involvement with the scandal-plagued Wedtech Corp. The investigation has expanded to include his involvement in a $1 billion Iraqi pipeline project.

Meese has predicted repeatedly he won’t be indicted and has said he won’t resign.

The resignations weren’t prompted by any new knowledge on the part of Burns or Weld that Meese is about to be indicted in the probe or that McKay has uncovered new evidence of possible culpability by the attorney general, several department sources said.

But they said both men believe major issues in the Justice Department aren’t being resolved and that the attorney general is inceasingly preoccupied with the criminal investigation.

Burns has taken a central role in day-to-day operations of the department, while Meese’s time increasingly has been taken up in meetings with his lawyers and grand jury appearances.

Burns and Weld arrived at the decision to resign independently of each other but agreed to quit during conversations Monday, said two sources who demanded anonymity.