Senate Judiciary Committee Chairman Lindsey Graham (R-SC) holds a news conference to discuss the summary of special counsel Robert Mueller's investigation at the U.S. Capitol March 25, 2019 in Washington, DC.

Attorney General William Barr needs to follow a multistep redaction process before he can release additional details from Robert Mueller's report on the Russia probe, Sen. Lindsey Graham said Wednesday.

Graham, chairman of the Senate Judiciary Committee and a close ally of President Donald Trump, also said that "everything" that doesn't threaten the law or national security will be revealed.

But that may not be enough for Democratic lawmakers, who have demanded that Trump's recently appointed attorney general release the special counsel report in its entirety.

Graham reportedly spoke with Barr and Trump on Tuesday night about the long-awaited report on Russia's election meddling and suspected Trump-campaign collusion during the 2016 campaign, as well as possible obstruction of justice by Trump. Barr's summary of the Mueller report said the special counsel cleared Trump and his campaign of collusion. Barr added, however, that Mueller did not exonerate Trump of obstruction of justice, although the attorney general decided that the evidence was insufficient to charge the president.

In a CNN interview Wednesday, Graham said Barr will first need to work through the report to remove information about Mueller's grand jury. Barr will then take that edited version to intelligence community officials and will also talk with prosecutors about further redactions.

"When he does that, which will take some weeks not months, he'll turn it over to the Senate and the House and he'll come before the Senate Judiciary Committee and he'll tell us about it," said Graham, R-S.C.

The Justice Department did not immediately respond to confirm Graham's description of Barr's redaction process.

Graham said that the redacted report will likely come "sometime in April."

"I have no idea how much grand jury material is there," Graham said. "Here's what I do know: You'll get everything that doesn't compromise national security or violate the law."

Graham also said Trump has no plans to invoke executive privilege before Mueller's report is released to Congress. Trump said to "just release it," Graham told CNN.

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Members of both parties had called on the Justice Department to publicly release as much of the special counsel's report as possible.

Shortly after the report was delivered by Mueller on Friday, Senate Minority Leader Chuck Schumer, D-N.Y., and House Speaker Nancy Pelosi, D-Calif., said in a statement that Barr should release it along with its "underlying documentation."

"Attorney General Barr must not give President Trump, his lawyers or his staff any 'sneak preview' of Special Counsel Mueller's findings or evidence, and the White House must not be allowed to interfere in decisions about what parts of those findings or evidence are made public," the Democratic leaders said.

Less than two weeks earlier, a nonbinding resolution to release the Russia report passed unanimously in the House, 420-0.

But for the second time this week, Senate Majority Leader Mitch McConnell, R-Ky., blocked a similar resolution introduced in the Senate by Democrats.

In a four-page summary sent Sunday, Barr wrote that Mueller's final report "did not find that the Trump campaign or anyone associated with it conspired or coordinated" with Russia. Trump and his political allies saw that conclusion as an unqualified victory that lends credence to the president's long-asserted refrain of "no collusion."

Mueller also made no determination on whether Trump himself obstructed justice, according to the summary. But Barr and Deputy Attorney General Rod Rosenstein, who received Mueller's report on Friday and reviewed it over the weekend, concluded that the special counsel's evidence was "not sufficient to establish that the President committed an obstruction-of-justice offense."