Newspapers will no longer have their sales figures automatically published, the industry's auditor has said.
The Audit Bureau of Circulations (ABC), which records and audits sales, usually publishes figures every month.
But ABC said publishers were growing concerned about a "negative narrative of decline" in newspaper sales.
Three major titles were absent from Thursday's figures, which showed a significant drop in sales in April amid the coronavirus pandemic.
The Telegraph, The Sun and The Times declined to publish, but other national titles revealed their figures as normal, including The Daily Express, The Daily Mirror, The Guardian, The Daily Star and The i Paper.
The Daily Mail had the highest sales of the papers which published, with a circulation of 945,000 - down from 1.13 million in March.
No national newspaper sold more than 1 million copies per day in the UK, as readers shopped less frequently under lockdown.
Newspapers were already suffering falling print sales prior to coronavirus, and stories about the gradual decline of newspapers have been common in recent years.
After the announcement that some papers would not publish their figures, The Guardian's media editor Jim Waterson said: "This is a genius move. Can't write about the decline in print newspaper sales if there's no longer evidence that print newspaper sales are actually declining!
"Entirely coincidentally, pre-Covid this was due to be the month the Sun lost its title as UK's biggest selling newspaper after 40+ years to Daily Mail. Now we've... no idea," he added.
All publishers will still have their circulation figures audited by ABC. As a result, newspapers will be able to tell advertisers what their sales are, regardless of whether or not they are made public.
Phil Smith, Director General of ISBA, which represents UK advertisers, said he "fully supported" the changes.
"These reporting updates will reduce the tendency for circulation to be seen as the only measure of Newsbrands' health in our multi-platform age," he said.
Newspapers have dramatically expanded their online operations in recent years in an effort to increase income from internet advertising.
'End of an era'
Analysis by David Sillito, media correspondent
It has been a difficult month for the newspapers. Traffic to websites may have risen but most papers are still heavily dependent on sales of print and many have seen a drop of around 30% over the last few weeks.
And it is not just sales revenue that has dropped, print advertising has also taken a nosedive.
But the decision to allow these figures to be a private matter between newspapers and advertisers is part of a bigger issue.
It's no secret the print newspaper business has been in long-term decline. Some are falling faster than others but over the last few years most have seen annual drops of around 7%.
The question for many is not if but when they stop the printing presses.
However, some papers, such as the New York Times, are showing that there may be a future with digital subscriptions. Digital advertising may also be a long term solution for some.
There are other ways then of measuring a news organisation's success and today's decision reflects that fact.
But this ever, it is also a little moment in the history of the British press. For years, the monthly sales figures were a proud boast to advertisers and politicians of a newspaper's power and reach. That era is over.