The public release of the Mueller report will take "weeks, not months," according to Reuters, citing a Justice Department official. 

Barr released a four-page summary of the report's central findings on Sunday, however he said he would need more time to review the report to determine what the public could see. Barr told Senate Judiciary Chairman Lindsey Graham (R-SC) of his plans to release the report publicly during a phone call this week. 

Meanwhile, there are conflicting reports over whether the White House will receive and advanced copy of the report - with Business Insider reporting that Barr told Graham that "he would send the special counsel Robert Mueller's final report on the Russia investigation to the White House before the public sees it, in case it wants to claim executive privilege over any parts." 

Reuters and NBC News, on the other hand, say there are no plans to let the White House see it in advance. 

Meanwhile, a debate has been brewing over Barr and Deputy AG Rod Rosenstein's decision to exonerate President Trump of obstruction in light of Barr's past comments on the subject. 

Barr on Sunday released his own summary of Mueller's report, which found that there was no evidence that the Trump campaign conspired with Russia during the 2016 election. Mueller declined to come to a conclusion on whether Trump obstructed justice in the Russia probe and instead laid out all the evidence prosecutors had collected before handing in his findings to Barr and Deputy Attorney General Rod Rosenstein.

Barr and Rosenstein then concluded that there was not sufficient evidence to determine that Trump obstructed justice. Their conclusion alarmed legal experts, who said Barr's past comments on the obstruction inquiry may have compromised his ability to make impartial decisions about that aspect of the investigation. -Business Insider

Barr sent a memo to the DOJ last year criticizing the obstruction probe as "legally insupportable," and advised that the Justice Department should not sanction it.