Washington (CNN) Special counsel Robert Mueller did not find Donald Trump's campaign or associates conspired with Russia, Attorney General William Barr said Sunday.

Mueller's investigation of whether the President committed obstruction of justice did not conclude the President committed a crime, but it also "does not exonerate him," Barr quoted from Mueller's report.

After nearly two years of being under the cloud of the Russia investigation, Trump's presidency is no longer directly under threat from the special counsel probe as the White House turns toward the 2020 campaign, although he still faces the specter of more legal and congressional action from the other investigations that remain ongoing.

Trump and his allies charged that Mueller's report fully vindicated the President, while Democrats were already raising questions about Barr making the decision on obstruction, a signal that the fight and the fallout from Mueller's investigation is far from over.

Mueller did not make the decision himself on whether to prosecute the President on obstruction. Barr and Deputy Attorney General Rod Rosenstein made the determination the evidence was "not sufficient" to support prosecution.

The President went beyond the conclusions of Barr's letter, saying Sunday the findings were a "complete and total exoneration."

"No Collusion, No Obstruction, Complete and Total EXONERATION. KEEP AMERICA GREAT!" Trump tweeted

"It was just announced there was no collusion with Russia ... there was no collusion with Russia, there was no obstruction, none whatsoever," Trump said to reporters before flying back to Washington from West Palm Beach, Florida. "It was a complete and total exoneration. It's a shame our country had to go through this. To be honest, it's a shame your President had to go through this."

Trump added, "This was an illegal takedown that failed and hopefully somebody's going to be looking at the other side."

Barr submitted to Congress a four-page summary of Mueller's conclusions on Sunday, which stated: "The special counsel's investigation did not find that the Trump campaign or anyone associated with it conspired or coordinated with Russia in its efforts to influence the 2016 U.S. Presidential Election."

Mueller's team has no plans to issue any new indictments.

"The report does not recommend any further indictments, nor did the special counsel obtain any sealed indictments that have yet to be made public," the letter states.

Barr wrote that no one associated with the Trump campaign conspired or coordinated with the Russian government, "despite multiple offers from Russian-affiliated individuals to assist the Trump campaign.

Mueller defined coordination as an "agreement -- tacit or express -- between the Trump Campaign and the Russian government on election interference."

The special counsel's office employed a massive effort through the court system and in interviewing witnesses to reach its findings. In all, Mueller's team interviewed about 500 witnesses and obtained more than 3,500 subpoenas and warrants of various types -- the bulk of which were subpoenas -- and 13 requests to foreign governments for evidence.

Obstruction questions

Barr and Rosenstein said they could not bring a criminal case with proof beyond a reasonable doubt that Trump's actions obstructed a specific proceeding.

Barr notes the "absence of such evidence" related to crimes around the Russian election interference weighed on his decision regarding obstruction.

The letter stated that Mueller said he conducted a "thorough factual investigation" into obstruction.

"While this report does not conclude that the President committed a crime, it also does not exonerate him," Barr quotes Mueller as saying.

In his letter, Barr says that Mueller's investigation into obstruction of justice found the President's actions were not "done with corrupt intent."

"In cataloguing the President's actions, many of which took place in public view, the report identifies no actions that, in our judgment, constitute obstructive conduct, had a nexus to a pending or contemplated proceeding, and were done with corrupt intent, each of which, under the Department's principles of federal prosecution guiding charging decisions, would need to be proven beyond a reasonable doubt to establish an obstruction-of-justice offense."

Fight over Barr's findings and release of full report

Democrats have demanded that Barr make Mueller's full report public and provide the special counsel's underlying evidence to Congress. They are threatening to subpoena and take the Trump administration to court if they're not satisfied with what the Justice Department provides.

House Judiciary Chairman Jerry Nadler said Sunday his committee will call Barr to testify "in the near future."

"In light of the very concerning discrepancies and final decision making at the Justice Department following the Special Counsel report, where Mueller did not exonerate the President, we will be calling Attorney General Barr in to testify before @HouseJudiciary in the near future," the New York Democrat tweeted.

Mueller's findings, Nadler said, means it is up to Congress to determine the President's future.

"Seems like the Department of Justice is putting matters squarely in Congress' court," Nadler tweeted.

Barr said he intends to release as much as possible from the report. Mueller will be involved in the scrubbing of the report to remove secret grand jury material and any content related to ongoing investigations before it could be made public, Barr wrote.

"Given these restrictions, the schedule for processing the report depends in part on how quickly the Department can identify the (grand jury) material that by law cannot be made public. I have requested the assistance of the Special Counsel."

The special counsel's investigation ended Friday after Mueller submitted his confidential report to Barr for review.

Additional legal investigations

The 22-month special counsel probe led to charges against 37 defendants, which included six Trump associates, 26 Russians and three Russian companies. Seven defendants have pleaded guilty, and one, Trump's former campaign chairman Paul Manafort, was convicted at trial.

While Mueller's investigation is over, several criminal investigations are still ongoing.

They relate to an alleged Russian conspiracy to blast political propaganda across Americans' social media networks; Manafort's political colleague from Russia, Konstantin Kilimnik; and what Manafort's deputy and a central Trump political player, Rick Gates, knows, according to court records.

Another is a grand jury's pursuit of documents from a company owned by a foreign government. That subpoena for documents began with Mueller last year.

The DC US Attorney's Office will pick up many of the open court cases, including Gates and former Trump adviser Roger Stone. And the US Attorney's Office in Manhattan continues to look into Trump's inauguration and allegations waged by Trump's former attorney and fixer Michael Cohen.