The Daily Mirror sold 1,742,378 copies, down 2.14% on May's 1,780,554, although still better than its performance in each of the three months from February to April.
However, the Sunday Mirror fell under the 1.5m copy threshold with a 3.9% decline over the month to 1,485,485, and The People lost 1.99% to 913,618.
Year on year, the six-month average circulation of the Sunday Mirror is down 3.36%, The People is down 7.1% and the Daily Mirror is down 7.72%.
Trinity Mirror also saw declines for its Scottish titles, with the Daily Record down 1.15% to 462,472, and the Sunday Mail down 0.62% to 553,894.
The company is reported to have blocked several approaches for the Daily Mirror from conference magnate Marcus Evans, while some shareholders are believed to be keen for it to focus on its regional newspapers and sell off the nationals.
The picture for the rest of the newspaper owners is also grim, with The Guardian suffering a marked fall of 2.99% to 361,408, The Daily Telegraph down 1.3% to 903,772 and the Financial Times down 1.23% to 425,984.
The compact titles again proved resilient, with The Independent down just 0.35% to 262,124, and The Times down just 0.18% to 683,495.
News International will also be heartened to see The Sun stop recent falls with a virtually unchanged 3,230,652 copies, and Richard Desmond's Daily Star fall back 0.87% to 855,612.
In the mid-market, the Daily Express lost 0.58% to 893,184, as it cut back around 17,000 of its bulk copies. July should see the remaining 44,500 bulks cut from the figures. Its rival the Daily Mail lost 0.38% to 2,350,012.
Associated Newpapers experienced a big fall at the London Evening Standard, down 4.69% to 332,524, while the Standard Lite's circulation was 76,831.
In the Sunday market, rises were seen for the Sunday Express, up 1.33% to 931,608, and the Sunday Telegraph, where Dominic Lawson was replaced as editor by Sarah Sands in June. The paper was up 1.28% to 674,531.
Its rival, The Sunday Times, fell 1.83% to 1,325,292 copies, while The Independent on Sunday was down 0.29% to 206,007 and The Observer was down 0.14% to 441,197.
The Mail on Sunday remained virtually unchanged at 2,253,480.
The News of the World was down 2.47% to 3,563,073 and the Daily Star Sunday was up 0.04% to 420,905.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the .