In a series of tweets, Mr Trump said: "Russia has never tried to use leverage over me. I HAVE NOTHING TO DO WITH RUSSIA - NO DEALS, NO LOANS, NO NOTHING!
"I win an election easily, a great "movement" is verified, and crooked opponents try to belittle our victory with FAKE NEWS. A sorry state!
"Intelligence agencies should never have allowed this fake news to "leak" into the public. One last shot at me. Are we living in Nazi Germany?"
Mr Trump is due to hold his first news conference as president-elect later on Wednesday.
Last week, US intelligence agencies reportedly presented the new claims - in the form of a two-page synopsis - to the president-elect, to President Barack Obama and to congressional leaders, CNN said on Wednesday.
The 35-page dossier of memos was published in full by Buzzfeed.
In the same briefing last week, US intelligence agencies released another unclassified report saying Russia ran a hacking campaign to influence the US presidential elections.
The latest allegations say Russia has damaging information about the president-elect's business interests, and salacious video evidence of his private life, including claims of using prostitutes at the Ritz-Carlton hotel in Moscow.
Other claims included in the 35-page dossier suggest Trump aides were involved with the alleged Russian hack of the Democratic Party of his rival Hillary Clinton.
Michael Cohen, a lawyer to Mr Trump named in the memos, has denied a specific claim that he went to Prague in August or September 2016 to meet Kremlin representatives to talk about the hacking.
"I've never been to Prague in my life. #fakenews," he tweeted.
Reince Priebus, Mr Trump's chief of staff, called the dossier report "phoney baloney garbage".
US media suggest the videos were prepared as "kompromat" - compromising material collected about a politician or public figure in order to create a threat of negative publicity, if needed.
The allegation that Mr Trump was vulnerable to blackmail and was being manipulated financially or otherwise is astonishing, says the BBC's Paul Wood in Washington.
In a campaign that was unprecedented, this goes to new extremes, our correspondent adds.
How this came to light
The allegations began circulating in political and media circles in recent months.
The BBC understands they are based on memos provided by a former British intelligence officer for an independent organisation opposed to Mr Trump in Washington DC. Sources say the CIA regards them as "credible".
The original intention was to derail Mr Trump's candidacy, reports say.
The BBC first saw the documents in October but has been unable to verify the claims included. Several material inaccuracies have been highlighted in them.
However past work by the British operative was considered by US intelligence to be reliable, US media say.
Donald Trump's son-in-law, Jared Kushner, will be senior adviser to the president, a senior transition official told CNN Monday.
The 35-year-old businessman-turned-political strategist played a key part in his father-in-law's presidential campaign and his new position is expected to test the limit of federal anti-nepotism rules.
US authorities have charged a US army veteran accused in a deadly shooting rampage at the Fort Lauderdale International Airport, with offences that could carry the death penalty, while continuing to probe whether "terrorism" was a potential motive.
Federal prosecutors charged Esteban Santiago on Saturday with firearms offenses and carrying out an act of violence at an airport, US Attorney Wifredo Ferrer said in a statement.
If convicted, he could face the death penalty or life in prison.
Santiago, 26, was accused of killing five, wounding six and sending thousands scrambling for safety on Friday before authorities shut down the airport in Florida, a major gateway to the Caribbean and Latin America.
The suspect was scheduled to make an initial court appearance on Monday.
Murder charges could be forthcoming from state prosecutors, but no decision has been made yet, according to the Sun Sentinel newspaper.
Santiago had travelled from Alaska to Fort Lauderdale on Friday.
After retrieving a 9mm semi-automatic handgun and ammunition that he had declared and stowed inside his checked luggage, he allegedly loaded the weapon in a bathroom and opened fire in the crowded baggage claim area.
FBI special agent George Piro said law enforcement was continuing to investigate motives for the attack, including "continuing to look at the terrorism angle".
A former member of the Puerto Rico and Alaska National Guard, Santiago served in Iraq from April 2010 to February 2011. He ended his service in August.
An aunt, Maria Luisa Ruiz, told the NorthJersey.com news site that Santiago became a father to a baby boy in September - and that he was having mental problems.
"Like a month ago, it was like he lost his mind," Ruiz said. "He said he saw things."
On November 7, Santiago walked into the FBI's Anchorage office and complained that his mind was being controlled by national intelligence agencies, which were forcing him to watch videos of the Islamic State of Iraq and the Levant (ISIL, also known as ISIS).
The "erratic behaviour" led agents to contact local police, who took him to a medical facility for a mental health evaluation, Piro said.
He was not placed on a no-fly list.
Anchorage police chief Christopher Tolley said Santiago came to the FBI office with a loaded magazine, but left his gun and newborn child in his car.
Santiago's weapon was taken by police for safekeeping at the time, and he was able to reclaim it on December 8.
Santiago's brother, Bryan, criticised the way authorities handled his case.
"They had him hospitalised for four days and they let him go. How are you going to let someone leave a psychological center after four days when he said he hears voices that the CIA is telling him to join certain groups?" Bryan Santiago told CNN, in a Spanish-language interview the network translated into English.
"Not everyone has the same reaction when they return from war. Some are better, and some, not so much."
The shooting renewed anxieties about airport security - a concern that has loomed large in the post-9/11 era - and shed new light on ongoing US gun-control debates.
The Transportation Security Administration -- the agency responsible for security at United States airports - allows passengers to travel with unloaded firearms and ammunition as checked baggage.
Senator Chris Murphy, a Democrat from Connecticut, rebuked the government for not taking legislative action to tighten gun laws.
"Political cowardice is the accomplice of every mass shooter," he wrote on Twitter.
The US has identified the Russian agents behind alleged hacking ahead of the presidential election won by Donald Trump in November, reports say. The agents, whose names have not been released, are alleged to have sent stolen Democratic emails to WikiLeaks to try to swing the vote for Mr Trump.
A prison riot in the Brazilian Amazon has left at least 56 people dead with some bodies decapitated and burned, officials said. The riot erupted on Sunday afternoon and lasted for 17 hours in the Anisio Jobim Penitentiary Complex (Compaj) in Manaus, the capital of Amazonas state.
A leading US Republican says she fears for the future of her seven grandchildren with Donald Trump in the White House. Christine Todd Whitman, head of the US Environmental Protection Agency (EPA) under George W Bush, accused Mr Trump of ignoring compelling science.
Donald Trump surpassed the necessary 270 votes in the Electoral College on Monday, taking the next step in the official process to become President.
Trump received 304 electoral votes to Hillary Clinton's 227. Seven "faithless" electors voted for other candidates, costing Trump two votes and Clinton four. Hawaii's votes -- three for Clinton and one breaking from the state's results and supporting Bernie Sanders -- were the last to be counted.
The US electoral college is expected to certify Donald Trump as president on Monday, despite a last-minute effort to thwart the Republican. The institution's 538 electors will vote at state capitols nationwide.
Universities and colleges in several US states are considering labelling themselves "sanctuary campuses" amid fears from immigrant students and pressure from activists following the election of Donald Trump.