The Sun sold more than 3.25 million copies of its new Sunday title yesterday, Rupert Murdoch said.
The media tycoon made the announcement on Twitter a day after the much-anticipated new edition hit newsstands for the first time.
The News International boss wrote: "Amazing! The Sun confirmed sale of 3,260,000 copies yesterday.
"Thanks all readers and advertisers. Sorry if sold out - more next time."
The sales are likely to be unwelcome to its rival publications, which include the Sunday Mirror and People.
But a spokesman for Trinity Mirror, which publishes both titles, refused to comment on whether it would lead to their prices being brought down.
He said he did not have figures available for how many copies they each sold yesterday.
Murdoch previously said he would be "very happy" if the Sun sold more than 2m copies.
The new edition, which replaces the News of the World, was launched with a pledge of "trust" and "decency" following the damaging phone-hacking scandal.
It promised readers it would remain "fearless, outspoken, mischievous and fun".
The newspaper claimed it would hold all journalists to account and said it had appointed a readers' champion to deal with errors and feedback from the public.
Above: Murdoch launching the new paper in 2012, and a similar scene when launching the first Sun tabloid under Murdoch on 17 November 1969.
A spokeswoman for News International said the figure quoted by Murdoch on Twitter came from "unaudited estimates" from projected sales.
The new Sun tipped the balance in the lucrative Sunday market after announcing it would be sold for just 50p, prompting a number of rivals to slash their prices.
The Daily Star Sunday had "your best value paper - 50p" emblazoned across it, while the Sunday Express read: "30p cheaper than the Mail on Sunday" written in a prominent font on the front page.
Although the People and Sunday Mirror kept their £1 price tag, they both offered a half-price promotion in three areas of the UK, but the Trinity Mirror spokesman would not comment on whether this would be done in future.
A spokesman for the Daily Star Sunday said it would not reveal how many copies it sold yesterday.
In an editorial, the new Sun commented on the arrests of 10 current and former employees over alleged corrupt payments to public officials, saying they were "innocent until proven guilty".
It said that the closure of the News of the World, which ceased publication last July at the height of the hacking scandal, was a "sobering experience".
The editorial, titled "A new Sun rises today", said: "As we launch the seven-day Sun, we want to strengthen that connection (with the readers) with a new independent Sun Readers' Champion to accept feedback and correct significant errors.
"Our journalists must abide by the Press Complaints Commission's editors' code, the industry standard for ethical behaviour, and the News Corporation standards of business conduct.
"We will hold our journalists to the standards we expect of them. After all, a newspaper which holds the powerful to account must do the same with itself.
"You will be able to trust our journalists to abide by the values of decency as they gather news."
It said the Sun has been a "tremendous force for good", adding: "It is worth reminding our readers, and detractors, of that as we publish our historic first Sunday edition during what is a challenging period.
Murdoch, 80, travelled to the paper's printers in Broxbourne, Hertfordshire, on Saturday night to witness the new Sunday tabloid roll off the press for the first time.
The front page of the new title featured an exclusive interview with Britain's Got Talent judge Amanda Holden, the first after the birth of her daughter, which left her in a critical condition in hospital.
The newspaper, which contained 92 pages and a 28-page football pull-out, also featured a topless photo of singer Kelly Rowland on page three, but the X Factor judge was covering her modesty.