At the weekend, News Corporation chief executive Murdoch personally oversaw the seventh day edition of the tabloid paper. He spent yesterday morning touring newsagents across Central London to see how the launch had gone down, and then visited a large WH Smiths at the Westfield Centre in Shepherd's Bush to check on sales.
The major multi-million pound advertising campaign for The Sun on Sunday appears to have worked, as Murdoch tweeted yesterday evening: "Reports early, but new Sun edition sold 3m!"
Edited by Dominic Mohan, the new 50p paper led with an interview with Amanda Holden about how she nearly died giving birth to her daughter. Should Murdoch prove correct, then it would have sold its entire three million print run.
This would represent a resounding return to the lucrative Sunday papers market for Murdoch's News International publisher, following the decision to shut down the News of the World last July at the height of the phone hacking scandal.
News International pulled in some celebrity columnists for the new paper, including chef Heston Blumenthal, the Archbishop of York, John Sentamu, "fashion expert" Nancy Dell'Olio, retired footballer Roy Keane and political writer Toby Young.
Katie Price used her column in the paper to pay tribute to Sunday Times journalist Marie Colvin, who was killed in Syria earlier in the week.
"She was just the sort of woman who impresses me - utterly fearless," wrote Price.
However, the first edition of the Sunday title has received a pretty poor reaction from media commentators, including former Sun editor Kelvin MacKenzie criticising its lack of kiss-and-tell stories. He told the BBC's Andrew Marr show: "I like sleaze on Sunday so I feel slightly robbed."
Media commentator Roy Greenslade said that the new paper was "bland" and read like a cross between Hello! and Take A Break magazines.
"Sunday papers are going out of fashion anyway, both tabloid and broadsheets, and it will be interesting to see if he (Rupert Murdoch) can turn that around," Greenslade told BBC Radio 4.
He added: "What struck me is the paper's soft focus. Everyone is mentioned in a very kind way. There is a clear intention to draw a line under the News of the World and that type of intrusive journalism."
Writing in the Financial Times, Matthew Engel described The Sun on Sunday as "timid, mumbling, joyless and dull".
He continued: "In the British market, seven-day-a-week journalism has always been an expression of despair - a triumph of accounts over editorial.
"No Sunday paper has achieved real success when produced, as this one is, by weary daily hacks for whom it is just another shift."
The Observer's Peter Preston said that The Sun on Sunday was short of the quality journalism that featured in the News of the World.
"There isn't much in the way of new thought: just Katie Price telling us that 'Kids need love… not posh school'," he wrote.
"The Archbishop of York cries, 'Let's all embrace a new beginning'. If there's a theme, it's that the Sunday version is keener on women's interests than its weekday lads' mag equivalent. But the pace is seven-day frenetic. You don't feel a moment's relaxation.
"The latest Sunday has been pumped up on adrenaline - and seems notably short of the quality that made the News of the World so dominant."