U.S. President Donald Trump, striking a defiant tone on Thursday after days of political tumult, denied asking former FBI Director James Comey to drop a probe into his former national security adviser and decried a "witch hunt" against him.

Trump's terse denial followed reports by Reuters and other media about a memo written by Comey alleging that Trump made the request to close down the investigation into Michael Flynn and Russia in February. Trump fired Comey on May 9.

"No. No. Next question," Trump told a news conference in the White House, when asked if he "in any way, shape or form" ever urged Comey to end the probe.

Comey's dismissal last week set off a series of jarring developments that culminated on Wednesday in the Justice Department's appointment of a special counsel to probe possible ties between Russia and Trump's 2016 presidential campaign.

They included media reports that Trump discussed sensitive intelligence on the Islamic State militant group with Russia's foreign minister.

In a pair of morning Twitter posts and at a later news conference, the Republican president described calls by some on the left for his impeachment as "ridiculous" and said he had done nothing to warrant criminal charges.

"The entire thing has been a witch hunt and there is no collusion between certainly myself and my campaign - but I can always speak for myself - and the Russians. Zero," he told the news conference, standing alongside Colombian President Juan Manuel Santos.

In his earlier Twitter posts, Trump criticized the naming of former FBI Director Robert Mueller as a special counsel by Deputy Attorney General Rod Rosenstein, an official he himself appointed.

"With all of the illegal acts that took place in the Clinton campaign & Obama Administration, there was never a special counsel appointed!" Trump wrote on Thursday morning.

He did not offer any evidence of such acts in his reference to former Democratic President Barack Obama and former presidential candidate Hillary Clinton.

"This is the single greatest witch hunt of a politician in American history!" Trump tweeted.

Democrats rejected Trump's characterization.

"This is a truth hunt," said Democratic Senator Amy Klobuchar.

Russia has denied U.S. intelligence agencies' conclusion that it interfered in the election campaign to try to tilt the vote in Trump's favour. Trump has long bristled at the notion that Russia played any role in his November election victory over Clinton.

Trump fired Flynn on Feb. 14 for misleading Vice President Mike Pence about the extent of his conversations last year with Russia's ambassador.

Reuters reported on Thursday that Flynn and other Trump campaign advisers were in contact with Russian officials and others with Kremlin ties in at least 18 calls and emails during the last seven months of the presidential race.

U.S. stocks recovered ground on Thursday as upbeat economic data emboldened investors to return to the market, a day after Wall Street saw the biggest selloff in eight months on worries the political turmoil could undermine Trump initiatives such as tax cuts that investors see as favouring economic growth.

DIVIDING THE COUNTRY

Rosenstein, the No. 2 Justice Department official, named Mueller amid mounting pressure in Congress for an independent investigation beyond existing FBI and congressional probes into the Russia issue.

Trump later told news anchors at the White House that Mueller's appointment was a "very, very negative thing," adding:

"I believe it hurts our country terribly, because it shows we're a divided, mixed-up, not-unified country."

Rosenstein briefed senators on Thursday but made no public comments. One of the attendees, speaking on condition of anonymity, described Rosenstein as anxious and nervous and said he drank multiple glasses of water "and spilled one."

Afterward, Republican Senator Lindsey Graham told reporters that "everything he said was that you need to treat this investigation as if it may be a criminal investigation."

A self-described friend of Comey's wrote in a public blog post on Thursday that Comey had told him that he had rebuffed a Trump request for loyalty by promising only honesty.

"He also told me that Trump was perceptibly uncomfortable with this answer," wrote Benjamin Wittes, a senior fellow at the Brookings Institution and a critic of Trump.

"And he said that ever since, the President had been trying to be chummy in a fashion that Comey felt was designed to absorb him into Trump’s world - to make him part of the team."

Democratic Senator Claire McCaskill said Rosenstein told senators that he knew Comey would be fired before he wrote his letter accusing him of missteps as FBI director, including his handling of an election-year probe into Clinton's use of a private email server while she was secretary of state.

The White House initially said last week that Trump was prompted to fire Comey after reading the Rosenstein letter. Trump later said he had already decided to dismiss him and was thinking of "this Russia thing."

The New York Times reported on Thursday that Trump called Comey weeks after he took office on Jan. 20 and asked him when federal authorities were going to say Trump was not under investigation. It cited two people briefed on the call.

Comey told Trump he should not contact him directly about FBI investigations but follow procedure and have the White House counsel ask the Justice Department, which oversees the FBI, the Times reported.

A key issue Mueller may have to tackle is whether Trump has committed obstruction of justice, an offence that could be used in any effort in the Republican-led Congress to impeach him and remove him from office.

Asked about possible obstruction of justice, Republican House of Representatives Speaker Paul Ryan told reporters the special counsel would "follow the facts where ever they may lead" and that "it is premature to prejudge anything at this point."