But in his denial, Trump added a qualifier that seemed to leave open the question of involvement by others in his campaign.
"The entire thing has been a witch hunt", he told the news conference, while standing beside Colombian President Juan Manuel Santos.
Dunford, whose first term will be completed in September, was picked for the job by President Barack Obama. In February national security adviser Michael Flynn was forced to resign after it emerged he had misled members of the administration about his contact with the Russian ambassador to the US.
The White House did not comment on the authenticity of Trump's conversation with the Russian officials in the Oval Office on May 9.
It said one official had read quotations to the Times and another had confirmed the broad outlines of the discussion.
The president did not announce his pick for Federal Bureau of Investigation director before leaving Friday on his first foreign trip. Laying aside the fact that Spicer is also connecting Comey's firing to the Russian Federation investigation, which only makes the obstruction suspicions stronger, if the White House wanted less "grandstanding" and more investigating why did it oppose the appointment of a special counsel?
"As the president has stated before - a thorough investigation will confirm that there was no collusion between the campaign and any foreign entity", White House Press Secretary Sean Spicer said in a statement in response to the Post story.
In a separate news report on Friday, the Washington Post claimed that a senior White House adviser was a person of significant interest in the investigation into possible ties between Trump's election campaign and Russian Federation.
And The New York Times said the United States president had told top Russian officials Mr Comey's sacking had relieved "great pressure" on him.
He also reportedly divulged sensitive classified information about the fight against ISIS from an ally, later revealed to be Israel, that the USA had not shared with other close partners.
The president has been adamant that the meddling did not alter the outcome of the race, but it has become a political cudgel for his opponents.
Robert Mueller, who served as FBI chief under George W Bush, was appointed this week as special counsel for the investigation.
"This is an extraordinary release of what are meant to be private conversations", Allen said.
Comey had courted controversy during the 2016 presidential polls when he revealed a renewed investigation into Hillary Clinton's email use, which the Democrats claimed had hurt her chances of becoming the president. Trump has denied any collusion and called the case a waste of money and time. Law-enforcement officials would not further identify the person.
Mr Trump clearly knew what he wanted to say as he took a few questions at a news briefing with visiting Colombian President Juan Manuel Santos.
USA stocks immediately pared gains after the reports but still closed higher for a second straight day.
"This is what OBSTRUCTION looks like", Sen.
An Obama administration official told CNN "This was a five-alarm fire from early on, the way the Russians were talking about him".