Donald Trump claims he has been completely exonerated by an inquiry into allegations Russia conspired to help him win the 2016 election.
A summary of Special Counsel Robert Mueller's long-awaited report released on Sunday found the Trump campaign had not conspired with Russia.
However it was inconclusive on whether Mr Trump had obstructed justice.
The Russia allegations had cast a shadow over Mr Trump's presidency and his chances of re-election in 2020.
Opposition Democrats are demanding full access to Mr Mueller's report, which was summarised for Congress by Attorney General William Barr.
White House spokeswoman Sarah Sanders said Mr Trump would let Mr Barr decide what to release but the president himself was "more than happy for any of this stuff to come out".
The report was the culmination of two years of investigation by Mr Mueller which saw some of the president's closest former aides prosecuted and, in some cases, imprisoned, although not for collusion with Russia.
Speaking at Palm Beach International Airport in Florida, Mr Trump declared: "There was no collusion with Russia. There was no obstruction... It was a complete and total exoneration."
"It's a shame that our country had to go through this," he added. "To be honest, it's a shame that your president has had to go through this. Before I even got elected it began and it began illegally."
Having repeatedly described the inquiry as a witch hunt, Mr Trump said it was an "illegal takedown that failed".
Republican Senator Lindsey Graham tweeted that it was a "great day for President Trump and his team".
"The cloud hanging over President Trump has been removed by this report," he said.
White House adviser Kellyanne Conway sent the president "congratulations" on Twitter, saying: "Today you won the 2016 election all over again. And got a gift for the 2020 election."
In his summary, Attorney General Barr writes, "The special counsel did not find that any US person or Trump campaign official conspired or knowingly co-ordinated with Russia."
But on the issue of whether justice was obstructed, Mr Mueller's report says: "While this report does not conclude that the president committed a crime, it also does not exonerate him."
Democratic House Speaker Nancy Pelosi and Senate Democratic Leader Chuck Schumer said in a joint statement that Mr Trump's claim that he had been "completely exonerated" was "not to be taken with any degree of credibility".
They called for full access to the Mueller report.
The Democratic Chair of the House of Representatives Judiciary Committee, Jerry Nadler, said he would ask Mr Barr to testify in front of the House Judiciary Committee "in the near future" over "very concerning discrepancies and final decision making at the Justice Department".
About a dozen other investigations are continuing into Mr Trump's activities. These include a federal inquiry in New York into possible election law violations by the Trump campaign and his businesses, and possible misconduct by the Trump inaugural committee.
Congress is also continuing its own inquiries, mostly in the Democratic-controlled House of Representatives.
Russia has denied being involved in hacking to influence the 2016 US election result.
Kremlin spokesman Dmitry Peskov mocked suggestions there had been collusion, saying: "I recall the words of the Chinese philosopher who said that it's hard to find a black cat in a dark room, especially if it's not there. Well, centuries pass and unfortunately they still don't understand that across the ocean."
Alexei Pushkov, a member of Russia's upper house, tweeted: "Democrats, Russophobes and leading media created a virtual conspiracy which existed only in their heads and in headlines, and nowhere else."
Legally, the House Judiciary Committee will want to get its hands on the full Mueller report. They will want to see why Robert Mueller felt he couldn't exonerate the president on obstruction of justice.
And remember, obstruction of justice is one of the "high crimes and misdemeanours" that can lead to impeachment.
There will be an endless back and forth over that. And I wouldn't be in the least bit surprised if the subpoenas start to fly.
Committees have the right to call people and papers. They are bound to flex their muscles as much as they can. They want to play this long. They want to damage the president.
To prosecute the president for obstruction of justice there would have needed to be evidence of intent to obstruct. So even though the president fired former FBI chief James Comey and unleashed regular torrents of abuse on Twitter about the investigation, if his only motivation for those acts was to vent his spleen rather than break the law, then he's done nothing wrong legally.