The report said Cohen acknowledged Trump's instructions when he was interviewed by the Mueller team.
The statement by Mueller's office on Friday night doesn't cite any specific errors. In it, the special counsel's spokesman, Peter Carr, said, "BuzzFeed's description of specific statements to the special counsel's office, and characterization of documents and testimony obtained by this office, regarding Michael Cohen's congressional testimony are not accurate."
BuzzFeed spokesman Matt Mittenthal said the publication stands by its reporting and urged readers to "stay tuned" as they worked to determine what Mueller was denying. Ben Smith, editor-in-chief of BuzzFeed News, also said the publication stands by its reporting and the sources who informed it.
"We urge the special counsel to make clear what he's disputing," Smith said.
Immediately after the special counsel's statement was issued, Trump retweeted several posts that called the story fake news. He later tweeted: "A very sad day for journalism, but a great day for our Country!"
Trump's lawyer, Rudy Giuliani, tweeted: "I commend Bob Mueller's office for correcting the BuzzFeed false story that Pres. Trump encouraged Cohen to lie. I ask the press to take heed that their hysterical desire to destroy this President has gone too far. They pursued this without critical analysis all day. #FAKENEWS."
The extraordinary statement from Mueller's office came after Democrats had vowed to investigate whether the report was true, calling that possibility a "concern of the greatest magnitude." House intelligence committee Chairman Adam Schiff, D-Calif., and House Judiciary Committee Chairman Jerrold Nadler, D-N.Y., both said they would probe BuzzFeed's account. Some Democrats even said that if the report were true, then Trump should be impeached.
The Associated Press had not independently confirmed the report. Any evidence that Trump directed a witness to lie to investigators would place him in the greatest political and legal jeopardy yet.
Giuliani said in a statement earlier Friday that "any suggestion — from any source — that the President counseled Michael Cohen to lie is categorically false." White House spokeswoman Sarah Huckabee Sanders called the allegation "absolutely ridiculous."
On Twitter on Friday morning, Trump charged that Cohen was "Lying to reduce his jail time!"
Cohen pleaded guilty in November to lying to Congress to cover up that he was negotiating the Trump Tower project on Trump's behalf during the heat of his presidential campaign. The charge was brought by Mueller and was the result of Cohen's cooperation with that probe.
Cohen admitted that he lied when he told lawmakers he had never agreed to travel to Russia in connection with the Moscow project and when he said that he'd decided by the end of January 2016 that the "proposal was not feasible for a variety of business reasons and should not be pursued further."
He was sentenced to three years in prison for crimes that included arranging the payment of hush money to conceal his boss' alleged sexual affairs, telling a judge that he agreed time and again to cover up Trump's "dirty deeds" out of "blind loyalty."
Giuliani noted that Cohen had pleaded guilty to lying and quoted federal prosecutors in New York who chastised him for a "pattern of lies and dishonesty over an extended period of time." Mueller's team, however, had previously called him a credible witness.
"Today's claims are just more made-up lies born of Michael Cohen's malice and desperation," Giuliani said.
Lanny Davis, a Cohen adviser, declined to comment.
Cohen is scheduled to testify publicly before the House Oversight and Reform Committee on Feb. 7. The top Democrat on the Senate intelligence committee, Virginia Sen. Mark Warner, said Friday that he expects Cohen to talk to that panel in February.
Although House Speaker Nancy Pelosi has discouraged any talk of impeachment in the early days of her new majority, some senior Democrats said that if the BuzzFeed report was confirmed, Trump's actions could rise to that level.
"If the @BuzzFeed story is true, President Trump must resign or be impeached," tweeted Texas Rep. Joaquin Castro, a member of the House intelligence panel.
Rhode Island Rep. David Cicilline, also a Judiciary committee member, tweeted that if Trump directed Cohen to lie, "that is obstruction of justice. Period. Full stop."
A Senate Democrat, Chris Murphy of Connecticut, tweeted that "we need to know this ASAP" if Mueller does have multiple sources confirming that Trump directed Cohen to lie.
"Mueller shouldn't end his inquiry, but it's about time for him to show Congress his cards before it's too late for us to act," Murphy tweeted.
Associated Press writers Jill Colvin and Zeke Miller in Washington and Jonathan Lemire and Jim Mustian in New York contributed to this report.