President Donald Trump on Wednesday continued to claim vindication in the Russia investigation moments after special counsel Robert Mueller gave his first public comments on the probe.

"Nothing changes from the Mueller Report," Trump tweeted. "There was insufficient evidence and therefore, in our Country, a person is innocent. The case is closed! Thank you."

Mueller said Wednesday that he did not come to a traditional prosecutorial decision on whether Trump obstructed justice in his report, explaining, as he did in that document, that he was bound by a Justice Department policy that prohibits charging a sitting president with a crime.

"If we had had confidence that he clearly did not commit a crime we would have said so," Mueller said. "We did not, however, make a determination to whether the president did commit a crime."

"The Constitution requires a process other than the criminal justice system to formally accuse a sitting president of wrongdoing," Mueller added, explaining the department policy — a reference to the constitutional provisions by which Congress may impeach and convict a president.

Beyond Justice Department policy, his team was guided by "principles of fairness," in that "it would be unfair to potentially accuse somebody of a crime when there can be no court resolution of an actual charge," he said.

Mueller, who also announced his resignation Wednesday, also said his report "speaks for itself" and "is my testimony," suggesting that any testimony of his before Congress would not provide information "beyond what is already public."

Mueller's remarks, however, challenge Attorney General William Barr's assertions in a summary of the report's key findings that he sent to Congress in March. In that memo, Barr said Mueller's decision not to reach a conclusion about whether Trump had tried to obstruct justice had left it him to him to review the evidence, which he found insufficient to support such a charge. But Mueller's remarks, as well as the report itself, referenced a role for Congress in checking the president.

After Mueller spoke, Trump's attorney Rudy Giuliani characterized his statement as a win for the president.

"A declination by any other name is a declination," Giuliani tweeted. "Mueller’s statement just repeated his report there is no case, collusion or obstruction. Despite DOJ policy on charging, he used over 430 pages and a brief press statement to reach that result. No case!!!"

A declination by any other name is a declination. Mueller’s statement just repeated his report there is no case, collusion or obstruction. Despite DOJ policy on charging, he used over 430 pages and a brief press statement to reach that result. No case!!! — Rudy Giuliani (@RudyGiuliani) May 29, 2019

Another of Trump's attorneys, Jay Sekulow, emphasized Barr's conclusion on the question of obstruction, saying in a statement after Mueller's remarks that the probe "produced no findings of collusion or obstruction against the President."

"The Attorney General conclusively determined that there was no obstruction by the President," Sekulow said. "In the words of Attorney General Barr: ‘the report identifies no actions that, in our judgment, constitute obstructive conduct.’”

White House press secretary Sarah Sanders echoed their comments, saying, "The report was clear— there was no collusion, no conspiracy — and the Department of Justice confirmed there was no obstruction."

"After two years, the Special Counsel is moving on with his life, and everyone else should do the same,” she added.

In his report, Mueller extensively detailed Russia's efforts to interfere in the 2016 election, multiple contacts between the Trump campaign and associates with Russians, and Trump's efforts to end the probe. Mueller wrote that the evidence he reviewed was not enough to establish a Trump-Russia conspiracy, and, on obstruction, said he could not come to a traditional prosecutorial decision because of Justice Department legal opinion.

"Accordingly, while this report does not conclude that the President committed a crime, it also does not exonerate him," Mueller wrote, later adding that Trump's "efforts to influence the investigation were mostly unsuccessful, but that is largely because the persons who surrounded the President declined to carry out orders or accede to his requests."

Rep. Jerrold Nadler, D-N.Y., the chairman of the House Judiciary Committee, said Wednesday that Mueller's statement reaffirmed the findings in his report and justified the congressional inquiries into the president's actions.

"Although Department of Justice policy prevented the Special Counsel from bringing criminal charges against the President, the Special Counsel has clearly demonstrated that President Trump is lying about the Special Counsel’s findings, lying about the testimony of key witnesses in the Special Counsel’s report, and is lying in saying that the Special Counsel found no obstruction and no collusion,” Nadler said in a statement.

"Given that Special Counsel Mueller was unable to pursue criminal charges against the President, it falls to Congress to respond to the crimes, lies and other wrongdoing of President Trump – and we will do so," he added. "No one, not even the President of the United States, is above the law."

Vice President Mike Pence's spokesperson, Alyssa Farah, countered Wednesday that Democrats were clinging to "discredited allegations," adding again that the Department of Justice "concluded there was no collusion and no obstruction."

"For two years, the White House fully cooperated with the investigation turning over millions of pages of documents and making witnesses available for hundreds of hours of testimony," Farah said.

"While some Democrats may cling to discredited allegations against the President, the American people can be confident: this Administration will continue to focus on making our nation stronger, safer, and more secure,” she added.