Mr Trump dismissed the claims, sending a tweet just as President Barack Obama commenced his farewell speech in Chicago saying: "FAKE NEWS - A TOTAL POLITICAL WITCH HUNT!"

Both the president-elect and President Obama have been briefed on the unsubstantiated allegations that are contained in a dossier based in part on memos put together by a British former spy who compiled them on behalf of anti-Trump Republicans.

But it is understood the British source is well regarded in US intelligence circles, and that intelligence chiefs have taken the allegations seriously enough not only to brief both the outgoing and incoming presidents, but to pursue an investigation into them.

According to the dossier, a source told the British operative that Mr Trump's "unorthodox behaviour in Russia over the years had provided the authorities there with enough embarrassing material on the [then] Republican presidential candidate to be able to blackmail him if they so wished".

It has been widely reported that Senator John McCain, an outspoken anti-Moscow hawk who has been critical of Mr Trump's apparent warmth towards Russian leader Vladimir Putin, passed the dossier to the FBI last month. The Guardian has also reported that the FBI sought warrants to tap the phones of individuals in Mr Trump's campaign due to their close ties with Russia.

CNN published a story about the contents of the dossier on Tuesday afternoon in the US, prompting the news website Buzzfeed to publish the dossier in full. Buzzfeed's editor-in-chief Ben Smith wrote in a letter to staff, later made public, that he had decided to publish the document because the dossier was already in wide circulation.

CNN reported the allegations "came, in part, from memos compiled by a former British intelligence operative, whose past work US intelligence officials consider credible" in a story by journalist Carl Bernstein, made famous for his work uncovering the Watergate scandal.

The broadcaster also reported that one reason for the intelligence briefings was to alert the president-elect to the fact that the dossier existed.

The Washington Post has reported that a senior US official with access to the document said that the allegations were presented at least in part to underscore that Russia appeared to have collected embarrassing information on both major candidates but released only material that might harm Democratic nominee Hillary Clinton — a reflection of Russian motivation that bolstered US spy agencies' conclusion that Moscow sought to help Mr Trump win.

According to allegations contained in the dossier, the FSB, Russia's principal security agency, gathered potentially compromising material of a sexual nature on Donald Trump while he was visiting Moscow in 2013 as host to the Miss Universe pageant. It says the activity referred to was "arranged/monitored" by the FSB.

It says Russian agents had been seeking to cultivate Mr Trump for five years "to encourage splits and divisions in [the] western alliance". It alleges that Mr Trump rejected "sweetener" real estate deals in Russia, but that his inner circle accepted a "regular flow" of information on his political rivals throughout the election.

Mr Trump has faced ongoing criticism for his closeness to Mr Putin and for his refusal to accept the findings of American intelligence agencies that during the campaign Russia hacked the computer system of the Democratic Party and leaked embarrassing information about Hillary Clinton in order to tilt the election in his favour. He was also criticised for publicly calling on Russia to find Mrs Clinton's so-called "missing emails".

The close connections of Paul Manafort, for a time the chairman of the Trump campaign, to Russia and the pro-Russia former Ukraine leader, Viktor Yanukovych, have also been questioned. In August last year the New York Times reported that Mr Manafort's name appeared in a ledger suggesting $US12.7 million in undisclosed cash payments had been designated for him by Mr Yanukovych's pro-Russian political party, for whom he worked as a consultant.

Neither the White House, the CIA, nor the Russian embassy in Washington DC, have responded to calls for comment, according to reports.