Trump, in a telephone interview late Saturday with Fox News, dismissed as "ridiculous" the Post story that alleged he went to great lengths to hide the content of his talks with Putin, even confiscating the notes of his interpreter and ordering that person to not discuss what was said.
Trump said he had "a great conversation" with Putin in Helsinki in July 2018.
When asked why not release details of the nearly two-hour conversation, Trump said: "I would, I don't with care.
"I mean, I had a conversation like every president does. You sit with the president of various countries... We were talking about Israel and securing Israel and lots of other things ... I'm not keeping anything under wraps, I couldn't care less. I mean, it's so ridiculous."
He added, "Anybody could have listened to that meeting, that meeting is up for grabs."
According to the Post, there is no detailed record of Trump's personal talks with Putin at five locations over the past two years.
The newspaper quotes unnamed current and former government officials as sources for the story.
Trump also told Fox when asked about Putin that "no collusion" has been found between his 2016 campaign and Russia, that he was a better candidate than Democrat Hillary Clinton, that the US economy "is the strongest in the world," and that The Washington Post is "basically the lobbyist for Amazon," as both are owned by billionaire Jeff Bezos.
A national security threat?
Trump also took aim at an earlier story in The New York Times stating that the FBI launched a previously undisclosed counterintelligence investigation to determine whether he posed a national security threat, at the same time that it opened a criminal probe into possible obstruction of justice.
The FBI investigation was later folded into the broader probe by Special Counsel Robert Mueller into Russia's meddling in the 2016 election and possible collaboration by the Trump campaign.
Fox asked if he had ever worked for Russia. "I think it's the most insulting thing I've ever been asked," he said, without directly answering the question.
He slammed the Times story as "the most insulting article I've ever had written and if you read the article, you'd see that they found absolutely nothing."
No evidence has publicly emerged that Trump was secretly in contact with or took direction from Russian officials, the Times said.
The FBI had been suspicious of Trump's ties to Russia during the 2016 campaign, but it held off on opening a probe until the president sacked Comey, who refused to roll back the Russia investigation, the Times said.
Mueller has indicted 33 people in the probe and convicted some of the president's close associates.
Trump's ex-national security advisor, Michael Flynn, has pleaded guilty to lying to investigators about his Moscow ties.
Trump's former personal lawyer, Michael Cohen, has been sentenced to three years in prison for multiple crimes, including felony violations of campaign finance laws that prosecutors allege were carried out under Trump's direction.
And Trump's former presidential campaign chairman, Paul Manafort, has been convicted in one case brought by Mueller and pleaded guilty in another, over financial crimes related to his work in Ukraine before the 2016 campaign, and for witness tampering.
The accusation had been made by the Washington Post. Trump said it was 'ridiculous'.