Attorney General William P. Barr will tell Congress on Wednesday that the special counsel did compile evidence of suspicious behavior by President Trump but that it was “not sufficient to establish” a crime was committed.

Mr. Barr, in written testimony released Tuesday night ahead of his 10 a.m. appearance before the Senate Judiciary Committee, defends his handling of special counsel Robert Mueller’s work and his 400-plus page report.

Mr. Barr said he felt he had to reach a conclusion on whether the president committed prosecutable crimes, even though Mr. Mueller did not. The attorney general said that’s the job of the Justice Department.

“We concluded that the evidence developed during the special counsel’s investigation is not sufficient to establish that the president committed an obstruction-of-justice offense,” he will say.

The “we” he refers to is himself and Deputy Attorney General Rod Rosenstein, the man who launched Mr. Mueller on his nearly two-year probe, and who oversaw it for most of that time, because Attorney General Jeff Sessions was recused.

Mr. Barr mentions the deputy attorney general five times in his four-page prepared statement.

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Mr. Rosenstein had been Democrats’ man for those months. They defended him against carping by Mr. Trump and warned that efforts to oust Mr. Rosenstein would spark a constitutional crisis.

Now Mr. Rosenstein finds himself in agreement with Mr. Barr, dashing Democrats’ hopes.

Mr. Barr will tell senators that the release of Mr. Mueller’s work ends the Justice Department’s work, save for a few loose-end cases against peripheral figures.

“From here on, the exercise of responding and reacting to the report is a matter for the American people and the political process,” he said. “As I am sure you agree, it is vitally important for the Department of Justice to stand apart from the political process and not to become an adjunct of it.”