The lawyers’ inquiry centers on why one of their colleagues, the deputy White House counsel John A. Eisenberg, placed a rough transcript of the call in a computer system typically reserved for the country’s most closely guarded secrets. Mr. Trump later directed that a reconstructed transcript be released amid intensifying scrutiny from House Democrats.

The review shows how quickly the impeachment inquiry escalated tensions in a West Wing already divided over the publication of the transcript, and it appears to be the latest example of administration officials rushing to protect themselves in the Ukraine scandal.

Some officials have expressed fears that the review is intended to assign blame and highlight decisions that helped fuel the impeachment inquiry, the people said. Mr. Eisenberg reacted angrily to suggestions that he is under scrutiny, according to two people told of his response.