News International's new Sunday edition of The Sun sold around 3.22 million copies when it launched on February 26 as the replacement for the News of the World, which was shut down last year at the height of the phone hacking scandal.
According to early unofficial industry estimates reported by The Guardian, the second edition of the tabloid paper is thought to have sold just over 2.6m yesterday.
The early estimates of between a 550,000 and 600,000 drop in sales, a fall of between 17% and 19%, suggests that the 50p tabloid is selling at roughly the same level as the News of the World, which had a circulation of around 2.66m before it closed last year.
On Saturday, Rupert Murdoch also said that a fall in week-on-week sales of around 15% would be a "great result" for the new paper.
"What will second Sunday edition of Sun sell? My guess down fifteen per cent would be a great result," he tweeted.
> The Sun on Sunday: Read Rupert Murdoch's email in full
Meanwhile, an influential commentator on Scottish politics has urged Alex Salmond to give the cold shoulder to support from Murdoch and his media empire.
Murdoch's newspapers have often played 'kingmaker' in politics, including Labour and the Conservatives having previously courted their support.
But Iain MacWhirter told Salmond to be very cautions about his new backer, as "Murdoch is the most toxic brand in British public life, his crude right-wing publications a byword for bent news and illegal practices such as phone hacking".
Writing in his Sunday Herald column yesterday, MacWhirter said that an "entire generation of politicians" have been corrupted by courting this "sinister oligarch".
He added: "Now we even have our own Scottish first minister worming his way into Rupert Murdoch's unsavoury inner circle, sending him cosy notes and free tickets, meeting his agents 26 times since 2007, trying to win favours from Murdoch's disreputable rags.
"Politicians always excuse this kind of ingratiating behaviour on the grounds that they have to keep the press on side; it's just how things are.
"Well, the first minister of Scotland needs to be reminded that this is not how things are here. Salmond should disown Rupert Murdoch if he doesn't want to hear Scottish voters saying, 'Ach, politicians. They're all the same'."