WASHINGTON—Special counsel Robert Mueller concluded that President Trump and his campaign didn’t conspire or coordinate with Russia to interfere in the 2016 election, according to a letter Attorney General William Barr sent to Congress on Sunday that summarized the final report on Mr. Mueller’s investigation.

But Mr. Mueller didn’t draw a conclusion on whether Mr. Trump obstructed justice, according to Mr. Barr’s letter, noting the report neither finds that the president committed a crime nor exonerated him. In the absence...