It is well documented that Bill Clinton has a propensity for being social when he sees someone he knows in public. But his decision to walk over to Attorney General Loretta E. Lynch for a chat at the Phoenix airport on Monday spurred a firestorm of Republican criticism.

The meeting was not preplanned, and Ms. Lynch told reporters that nothing sensitive was discussed.

But as attorney general, Ms. Lynch oversees the Justice Department, which oversees the F.B.I., which is looking into the circumstances around Hillary Clinton’s use of a private email server during her time as secretary of state.

The reaction to the meeting was so politically fraught that Ms. Lynch is expected on Friday to announce that she will rely on the recommendations of career prosecutors and the F.B.I for the outcome of the email investigation.