Attorney General Edwin Meese III temporarily filled five vacant posts in the Justice Department Monday, and in addition Francis Keating will be running the No. 3 office at the department by the end of the week, a spokesman said.

Keating is the assistant Treasury Department secretary nominated by President Reagan on Friday to become associate attorney general.Keating will move in to the post on an acting basis until confirmed by the Senate, said Justice Department spokesman Patrick Korten. He would replace Stephen Trott, who left earlier this month to become a federal appeals court judge.

Before leaving for speaking engagements in Detroit Monday, Meese appointed Grace Mastalli and C.H. Albright as assistants in the associate attorney general's office. Keating will choose his own deputies after he arrives.

Mastalli works in the executive office of U.S. attorneys and Albright has been a special assistant to Assistant Attorney General John Bolton, now in charge of the civil division.

Department aides James Byrnes, John Howard and Thomas Christina were named to fill three slots in the office of former Deputy Attorney General Arnold Burns.

Burns is one of two Justice Department officials who resigned in protest March 29 over Meese's continued tenure. Five of Burns' six deputies are leaving. Burns' last day on the job was Friday, two days after he and former Assistant Attorney General William Weld outlined their objections to Meese in a blunt face-to-face meeting with Reagan at the White House.