In it, Mr. Kelly did not directly address the case of the aide, Rob Porter, who was forced out of his job as the White House staff secretary this month after news reports that his two former wives had claimed physical and emotional abuse by Mr. Porter during their marriages.

The White House has been reeling for more than a week amid shifting explanations of how Mr. Porter was allowed to remain in one of the most sensitive posts there despite the F.B.I.’s discovery months ago of the abuse allegations.

The deepening scandal called into question the administration’s veracity as Republicans and Democrats pressured Mr. Kelly to detail what had happened. The memo does not do that.

But Mr. Kelly’s pledge of action comes after bipartisan pressure from lawmakers on Capitol Hill, who have in recent days demanded that the White House account for Mr. Porter’s case and the broader issue of people without permanent security clearances working at 1600 Pennsylvania Avenue.

“The committee is investigating the policies and processes by which interim security clearances are investigated and adjudicated within the executive branch,” Representative Trey Gowdy, Republican of South Carolina and the chairman of the House Oversight Committee, wrote this week.

Mr. Kelly said that he was putting into effect changes that would address a failure of communication between the F.B.I. and senior officials in the West Wing — exactly the kind of failure that White House officials have said was responsible in Mr. Porter’s case.

Among the most significant changes, Mr. Kelly ordered that F.B.I. officials would now directly report to the White House counsel, Donald F. McGahn II, any concerns that they uncovered during the background investigations of the president’s top aides.