Mr. Barr defended his descriptions of the special counsel’s conclusions in conversations with Mr. Mueller over the days that followed, according to two people with knowledge of their discussions.

The central issue in the simmering dispute is how the public’s understanding of the special counsel’s work has been shaped since Mr. Mueller ended his investigation and delivered his 448-page report to the attorney general, his boss and longtime friend.

What we don’t know: what specific objections Mr. Mueller raised in his letter. But a Justice Department spokeswoman said he “expressed a frustration over the lack of context” surrounding his findings on obstruction of justice.

What’s next: On Wednesday, Mr. Barr is scheduled to testify before the Senate Judiciary Committee about the investigation. Follow our live coverage at nytimes.com.