In response to a Twitter user’s inquiry over the claim, he said, “This is incorrect.”
After months of legal fighting, Mr. Musk finalised his $44 billion (£37.9 billion) acquisition of the social networking company last week.
The takeover resulted in the departure of the company’s senior executives, including its CEO, chairman, and finance head.
The New York Times reported over the weekend that Mr. Musk had authorised widespread employment layoffs at Twitter.
The publication said that the layoffs would occur prior to November 1, when staff were scheduled to receive substantial grants of company stock as part of their compensation packages.
The acquisition has spurred Twitter users to speculate about the platform’s future appearance under Mr. Musk’s leadership.
Some have expressed worry that more permissive free speech regulations might lead to the readmission of those banned for hate speech or misinformation.
Mr. Musk said last week that he did not want for the platform to become an echo chamber for hatred and discord. “Obviously, Twitter cannot become a free-for-all hellscape where anything can be spoken without repercussions,” he tweeted.
However, after refuting the New York Times article on job losses, Mr. Musk tweeted a screenshot of a New York Times headline claiming that he had posted a link to a “website known to promote fake news.”
The headline of the New York Times linked to a response that Mr. Musk sent and then removed over the weekend in response to a tweet by former US presidential contender Hillary Clinton.
His response included a link to a conspiracy theory about an attack on Nancy Pelosi’s husband, Paul Pelosi.
Separately, in answer to a query concerning users obtaining verified on the site and earning the coveted so-called “blue check mark,” he said that the procedure would be altered.
Mr. Musk said, without elaboration, that the whole verification process is undergoing a makeover.
It was stated that the company intended to charge users for verification.
Mr. Musk also initiated a Twitter poll asking his over 112 million followers whether he should revive the short-video application Vine.
In 2012, Twitter acquired the service that enabled users to post six-second looping recordings.
It had more than 200 million active members by the end of 2015 when the social media site discontinued it.
Mr. Musk has previously conducted polls to determine whether he should sell 10 percent of his stock in the electric vehicle manufacturer Tesla and if Twitter should have an edit button.