When asked during a press conference whether he had ever urged Comey to end the probe into former national security adviser Michael Flynn, Trump swiftly interrupted the reporter, saying, "No, no."

On Tuesday, US media reported that the former FBI chief had written a memo describing how Trump urged him to drop the probe into ties between Flynn and Russia. Trump allegedly told him during a White House meeting that "I hope you can let this go," referring to the investigation.

Trump fired Comey as head of the FBI last week, saying the dismissal was driven by a loss of faith in the bureau chief on behalf of both himself and the public.

The president said he thought the ousting would be greeted with bipartisan support. But the move has fuelled speculation that the president sought to deliberately stall the investigation Comey was leading.

'Witch hunt'

Trump also used Thursday's joint press conference with visiting Colombian President Juan Manuel Santos to decry the FBI's investigation into alleged collusion between his campaign and Russia, describing it as a "witch hunt" and denouncing it for "dividing the country."

The president repeated his denial of involvement with Russia during Thursday's press conference, saying, "There's been no collusion between certainly myself - and my campaign, but I can always speak for myself - and the Russians. Zero."

Trump had earlier released a statement saying he looked forward to the matter being concluded "quickly," following Wednesday's appointment of  ex-FBI Director Robert Mueller to lead the federal investigation into Russia's alleged election meddling.

US Deputy Attorney General Rod Rosenstein reportedly briefed senators on Mueller's appointment on Thursday, but refused to give a public statement. However,  Republican Senator Lindsey Graham told reporters after the briefing that "everything he (Rosenstein) said was that you need to treat this investigation as if it may be a criminal investigation."

Democratic Senator Richard Blumenthal also told reporters that Mueller was conducting a criminal investigation, including into whether there was any obstruction of justice on behalf of Trump's campaign team.

Read more: What you need to know about special counsel Robert Mueller's investigation into the Trump campaign

Trump to name new FBI chief

Trump also announced Thursday that he was "very close" to naming Comey's successor as FBI director, with ex-Democratic Senator Joe Lieberman expected to fill the post. 

Lieberman ran as Al Gore's vice presidential nominee in 2000, before he left the Democratic Party and was re-elected to the Senate as an independent.

The president gave few details on the announcement, commenting only that "the people in the FBI will be very, very thrilled" with his choice for the agency's new head.

Trump's nominee must first be confirmed by the Senate before he or she can fill the post.