In years past, the move by senior members of President Trump’s administration to share defense secrets over the Signal messaging app would have represented a serious breach that would have likely prompted investigations by the F.B.I. and the Justice Department’s national security division.

Yet so far, neither the attorney general, Pam Bondi, nor the F.B.I. director, Kash Patel, appear to be planning to investigate whether the communications described in a bombshell report in The Atlantic magazine on Monday potentially violated federal laws like the Espionage Act.

The bureau and the department have undertaken these kind of investigations to figure out the extent of damage to the country’s national security, uncover other instances of recklessness and examine whether laws have been broken. Such an inquiry would be independent from — and far more thorough than — the self-policing, in-house review by the National Security Council announced on Tuesday.

What Ms. Bondi and Mr. Patel do next is an important early test for two officials who promised during their confirmation hearings to administer justice impartially and free from political considerations that, in their view, led to criminal prosecutions of Mr. Trump during the Biden administration.

“This is something that would normally be investigated by the F.B.I. and D.O.J.,” said Mary McCord, a longtime senior official for the Justice Department who now teaches at the Georgetown University Law Center.