The Independent increased its paid-for sale by 23 per cent year on year to 228,697. However, it failed to post a significant sales increase on the previous month.
The Guardian is currently the hardest hit of the quality dailies, with a 5 per cent decline in sales to 363,638. The Daily Telegraph, meanwhile, lost 4 per cent of its sales as it fell to 873,181.
Robert Thomson, the editor of The Times, said of the national roll-out of its compact edition: "The Times compact is the UK's best-selling quality compact and the roll-out across the country means that more people than ever before will be able to try the new format."
However, The Times will continue to be published in its broadsheet format in all regions. Around half of its readers are still buying the broadsheet version.
Its compact version is only published Monday to Friday, with only a broadsheet version available on Saturdays.
Sales of the Daily Mirror appear to have suffered from the backlash over its publication of faked pictures supposedly showing abuse of Iraqi prisoners by British troops.
Its May circulation was 1,846,734, a 6 per cent year-on-year decline.
It lost an average of 42,000 sales a day over the course of the month.
Its editor, Piers Morgan, was subsequently sacked by the Daily Mirror owner, Trinity Mirror. It has yet to appoint a successor but reports suggest that the News of the World editor, Andy Coulson, has ruled himself out.
The Sun also suffered a significant decline, losing 5 per cent of its sales. It now sells 3,360,562 copies.
In the mid-market, sales of the Daily Mail and The Mail on Sunday were down by less than 1 per cent while the Daily Express sales fell 3 per cent to 878,529 copies.
Sales of quality Sunday titles were also down, with The Independent on Sunday and Sunday Telegraph the hardest hit. Both lost 3 per cent of their circulations.
The News of the World increased its sales by 1 per cent to 3,848,511 while the Sunday Mirror lost 2 per cent with an average sale of 1,565,778.