The MoS increased sales by one per cent year on year to 1.9m in June.
The News of the World, in its final full month of circulation, sold 2,667,428 copies - a 5.7 per cent drop year on year which was in line with the rest of the market.
A spokesperson for the Mail on Sunday said the circulation boost was largely the result of its Weekend Reward Club scheme launched last month. This works by offering shopping vouchers and other incentives to those who buy the paper.
The paper has confirmed it is increasing its print-run to three million copies this weekend following the closure of the News of the World, while the Daily Star Sunday is understood to be upping its print-run from 600,000 to more than two million.
Trinity Mirror-owned titles The People and Sunday Mirror are understood to be doubling their combined distribution to more than three million.
The Daily star saw the biggest fall in year-on-year circulation among national daily titles in June, down 12.6 per cent to 708,163, followed by The Times with a 12.5 per cent drop to 440,581.
National newspaper print circulations for June 2011 (source ABC)
(Figures are average circ, percentage change year on year)
Daily Mirror: 1,170,541; -6.3
Daily Record: 305,840; -5.4
Daily Star: 708,163; -12.6
The Sun: 2,806,746; -5.8
Daily Express: 621,871; -6.4
Daily Mail: 2,047,206; -2.2
The Daily Telegraph: 622,719; -8.6
Financial Times: 356,194; -9.1
The Herald: 48,465; -9
The Guardian: 256,283; -10.4
i: 173,165; N/A
The Independent: 176,681; -5.6
The Scotsman: 40,390; -8.9
The Times: 440,581; -12.5
Racing Post: 56,507; -4.3
Daily Star Sunday: 305,978; -13.1
News of the World: 2,667,428; -5.7
Sunday Mail: 360,475; -6.9
Sunday Mirror: 1,087,796; -5.2
The People: 474,549; -8.6
Sunday Express: 539,478; -4.8
Sunday Post: 302,420; -6.9
The Mail on Sunday: 1,927,791; +1
Independent on Sunday: 151,229; -3.8
The Observer: 288,928; -11.6
Scotland on Sunday: 51,053; -8.3
Sunday Herald: 29,233; -28.2
The Sunday Telegraph: 474,722; -6.7
The Sunday Times: 1,000,848; -7.8